Formula for Finding Specific Heat of Metal When You Know the Beginning Heat and Equilibrium
Heat Capacity
The heat chapters measures the corporeality of rut necessary to raise the temperature of an object or system by one caste Celsius.
Learning Objectives
Explain the enthalpy in a organisation with constant volume and pressure
Key Takeaways
Key Points
- Heat chapters is the measurable physical quantity that characterizes the amount of estrus required to change a substance's temperature by a given amount. Information technology is measured in joules per Kelvin and given by.
- The rut capacity is an extensive holding, scaling with the size of the system.
- The heat chapters of virtually systems is not constant (though it can often be treated as such). It depends on the temperature, pressure, and volume of the system under consideration.
Primal Terms
- heat chapters: The amount of heat energy needed to raise the temperature of an object or unit of measurement of matter past one degree Celsius; in units of joules per kelvin (J/G).
- enthalpy: the full amount of energy in a system, including both the internal energy and the free energy needed to displace its environment
Heat Capacity
Estrus capacity (unremarkably denoted by a capital C, often with subscripts), or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given corporeality. In SI units, rut capacity is expressed in units of joules per kelvin (J/K).
An object's heat capacity (symbol C) is defined as the ratio of the corporeality of heat energy transferred to an object to the resulting increase in temperature of the object.
[latex]\displaystyle{\text{C}=\frac{\text{Q}}{ \Delta \text{T}}.} [/latex]
Oestrus capacity is an extensive holding, then it scales with the size of the system. A sample containing twice the amount of substance every bit another sample requires the transfer of twice as much heat (Q) to achieve the same change in temperature (ΔT). For case, if it takes 1,000 J to heat a block of atomic number 26, it would have two,000 J to heat a 2d cake of iron with twice the mass every bit the first.
The Measurement of Heat Chapters
The heat capacity of most systems is non a abiding. Rather, information technology depends on the land variables of the thermodynamic system under report. In particular, it is dependent on temperature itself, as well as on the pressure and the book of the organisation, and the ways in which pressures and volumes have been allowed to change while the system has passed from i temperature to another. The reason for this is that pressure-volume work done to the system raises its temperature past a mechanism other than heating, while pressure-volume work done by the organization absorbs heat without raising the organisation'south temperature. (The temperature dependence is why the definition a calorie is formally the energy needed to heat 1 grand of h2o from 14.v to 15.v °C instead of generally by one °C. )
Different measurements of rut chapters can therefore be performed, well-nigh commonly at constant pressure level and constant volume. The values thus measured are usually subscripted (past p and V, respectively) to point the definition. Gases and liquids are typically also measured at abiding volume. Measurements under constant pressure level produce larger values than those at abiding volume because the abiding pressure values also include heat energy that is used to exercise work to aggrandize the substance against the constant pressure as its temperature increases. This difference is especially notable in gases where values nether constant pressure are typically 30% to 66.7% greater than those at constant volume.
Thermodynamic Relations and Definition of Oestrus Capacity
The internal energy of a closed organization changes either by calculation oestrus to the organization or by the arrangement performing piece of work. Recalling the showtime police of thermodynamics,
[latex]\text{dU}=\delta \text{Q}-\delta \text{Due west}[/latex].
For work equally a result of an increase of the organization volume we may write,
[latex]\text{dU}=\delta \text{Q}-\text{PdV}[/latex].
If the heat is added at constant volume, and then the second term of this relation vanishes and one readily obtains
[latex]\displaystyle{\left( \frac{\partial \text{U}}{\partial \text{T}}\right) _{\text{V}}=\left( \frac{\partial \text{Q}}{\partial \text{T}}\correct) _{\text{V}}=\text{C}_{\text{V}}}[/latex].
This defines the oestrus chapters at abiding volume, C V. Another useful quantity is the heat chapters at abiding pressure level, C P. With the enthalpy of the system given by
[latex]\text{H}=\text{U}+\text{PV}[/latex],
our equation for dU changes to
[latex]\text{dH}=\delta \text{Q}+\text{VdP}[/latex],
and therefore, at constant pressure level, we have
[latex](\frac{\fractional \text{H}}{\partial \text{T}})_{\text{P}}=(\frac{\partial \text{Q}}{\partial \text{T}})_{\text{P}}=\text{C}_{\text{P}}[/latex].
Specific Oestrus
The specific heat is an intensive property that describes how much heat must be added to a particular substance to raise its temperature.
Learning Objectives
Summarize the quantitative relationship between heat transfer and temperature modify
Central Takeaways
Key Points
- Different the total heat chapters, the specific heat capacity is independent of mass or volume. Information technology describes how much heat must be added to a unit of mass of a given substance to heighten its temperature by i degree Celsius. The units of specific oestrus capacity are J/(kg °C) or equivalently J/(kg K).
- The estrus chapters and the specific oestrus are related by C=cm or c=C/thousand.
- The mass yard, specific heat c, change in temperature ΔT, and rut added (or subtracted) Q are related past the equation: Q=mcΔT.
- Values of specific heat are dependent on the properties and phase of a given substance. Since they cannot exist calculated hands, they are empirically measured and available for reference in tables.
Central Terms
- specific heat capacity: The amount of heat that must be added (or removed) from a unit mass of a substance to change its temperature by one degree Celsius. It is an intensive belongings.
Specific Heat
The heat capacity is an extensive property that describes how much estrus free energy it takes to enhance the temperature of a given system. However, information technology would be pretty inconvenient to mensurate the heat capacity of every unit of measurement of thing. What we desire is an intensive belongings that depends but on the type and stage of a substance and can be applied to systems of arbitrary size. This quantity is known as the specific rut chapters (or merely, the specific oestrus), which is the heat chapters per unit mass of a textile. Experiments prove that the transferred oestrus depends on three factors: (1) The change in temperature, (two) the mass of the system, and (3) the substance and phase of the substance. The terminal 2 factors are encapsulated in the value of the specific rut.
Oestrus Transfer and Specific Heat Capacity: The heat Q transferred to cause a temperature change depends on the magnitude of the temperature modify, the mass of the arrangement, and the substance and phase involved. (a) The amount of heat transferred is directly proportional to the temperature modify. To double the temperature change of a mass m, you need to add twice the oestrus. (b) The corporeality of heat transferred is also directly proportional to the mass. To cause an equivalent temperature modify in a doubled mass, you need to add twice the oestrus. (c) The amount of heat transferred depends on the substance and its phase. If it takes an corporeality Q of oestrus to crusade a temperature change ΔT in a given mass of copper, it will take 10.8 times that amount of heat to crusade the equivalent temperature change in the same mass of water bold no phase change in either substance.
The dependence on temperature change and mass are easily understood. Because the (average) kinetic energy of an cantlet or molecule is proportional to the accented temperature, the internal energy of a system is proportional to the absolute temperature and the number of atoms or molecules. Since the transferred oestrus is equal to the change in the internal energy, the heat is proportional to the mass of the substance and the temperature alter. The transferred rut also depends on the substance so that, for example, the rut necessary to raise the temperature is less for alcohol than for water. For the same substance, the transferred heat also depends on the phase (gas, liquid, or solid).
The quantitative human relationship betwixt heat transfer and temperature change contains all three factors:
[latex]\text{Q}=\text{mc}\Delta \text{T}[/latex],
where Q is the symbol for rut transfer, one thousand is the mass of the substance, and ΔT is the alter in temperature. The symbol c stands for specific rut and depends on the material and stage.
The specific heat is the amount of heat necessary to change the temperature of i.00 kg of mass by i.00ºC. The specific heat c is a property of the substance; its SI unit is J/(kg⋅K) or J/(kg⋅C). Think that the temperature alter (ΔT) is the aforementioned in units of kelvin and degrees Celsius. Note that the total heat capacity C is simply the production of the specific heat capacity c and the mass of the substance chiliad, i.e.,
[latex]\text{C}=\text{mc}[/latex] or [latex]\text{c}=\frac{\text{C}}{\text{m}}=\frac{\text{C}}{\rho \text{5}}[/latex],
where ϱ is the density of the substance and V is its volume.
Values of specific heat must generally be looked upwards in tables, considering at that place is no simple way to summate them. Instead, they are measured empirically. In general, the specific heat also depends on the temperature. The tabular array below lists representative values of specific rut for various substances. Except for gases, the temperature and volume dependence of the specific heat of most substances is weak. The specific estrus of water is five times that of glass and ten times that of atomic number 26, which means that it takes 5 times every bit much heat to raise the temperature of water the aforementioned amount every bit for glass and ten times as much estrus to raise the temperature of h2o as for iron. In fact, water has one of the largest specific heats of any material, which is important for sustaining life on Globe.
Specific Heats: Listed are the specific heats of diverse substances. These values are identical in units of cal/(g⋅C).iii. cv at constant volume and at xx.0ºC, except as noted, and at one.00 atm average pressure. Values in parentheses are cp at a constant pressure of ane.00 atm.
Calorimetry
Calorimetry is the measurement of the heat of chemical reactions or physical changes.
Learning Objectives
Clarify the relationship between the gas abiding for an ideal gas yield and volume
Key Takeaways
Primal Points
- A calorimeter is used to measure the heat generated (or captivated) past a physical alter or chemical reaction. The science of measuring these changes is known as calorimetry.
- In club to do calorimetry, information technology is crucial to know the specific heats of the substances existence measured.
- Calorimetry can be performed nether abiding volume or constant pressure. The type of calculation washed depends on the weather condition of the experiment.
Fundamental Terms
- constant-pressure calorimeter: An musical instrument used to measure out the heat generated during changes that do not involve changes in pressure.
- calorimeter: An apparatus for measuring the heat generated or absorbed by either a chemical reaction, change of phase or some other concrete change.
- constant-volume calorimeter: An instrument used to measure the heat generated during changes that do not involve changes in volume.
Calorimetry
Overview
Calorimetry is the science of measuring the heat of chemic reactions or concrete changes. Calorimetry is performed with a calorimeter. A simple calorimeter merely consists of a thermometer attached to a metal container full of water suspended in a higher place a combustion bedchamber. The word calorimetry is derived from the Latin word calor, meaning heat. Scottish physician and scientist Joseph Black, who was the beginning to recognize the distinction between oestrus and temperature, is said to be the founder of calorimetry.
Calorimetry requires that the textile being heated have known thermal properties, i.due east. specific oestrus capacities. The classical rule, recognized past Clausius and by Kelvin, is that the pressure exerted past the calorimetric material is fully and rapidly determined solely by its temperature and volume; this dominion is for changes that do not involve phase change, such as melting of ice. There are many materials that practise non comply with this dominion, and for them, more complex equations are required than those below.
Water ice Calorimeter: The globe's offset ice-calorimeter, used in the winter of 1782-83, past Antoine Lavoisier and Pierre-Simon Laplace, to determine the heat evolved in variouschemical changes; calculations which were based on Joseph Black's prior discovery of latent heat. These experiments mark the foundation of thermochemistry.
Basic Calorimetry at Constant Value
Constant-volume calorimetry is calorimetry performed at a constant volume. This involves the employ of a constant-volume calorimeter (i blazon is chosen a Bomb calorimeter). For constant-volume calorimetry:
[latex]\delta \text{Q}=\text{C}_{\text{5}}\Delta \text{T}=\text{mc}_{\text{V}}\Delta \text{T}[/latex]
where δQ is the increment of heat gained past the sample, CV is the heat capacity at constant volume, c5 is the specific heat at constant volume, and ΔT is the modify in temperature.
Measuring Enthalpy Change
To detect the enthalpy change per mass (or per mole) of a substance A in a reaction between two substances A and B, the substances are added to a calorimeter and the initial and final temperatures (before the reaction started and after it has finished) are noted. Multiplying the temperature modify by the mass and specific oestrus capacities of the substances gives a value for the free energy given off or absorbed during the reaction:
[latex]\delta \text{Q}=\Delta \text{T}(\text{m}_{\text{A}}\text{c}_{\text{A}}+\text{k}_{\text{B}}\text{c}_{\text{B}})[/latex]
Dividing the energy change past how many grams (or moles) of A were present gives its enthalpy change of reaction. This method is used primarily in academic instruction as it describes the theory of calorimetry. It does non account for the heat loss through the container or the heat capacity of the thermometer and container itself. In addition, the object placed inside the calorimeter shows that the objects transferred their heat to the calorimeter and into the liquid, and the estrus absorbed by the calorimeter and the liquid is equal to the estrus given off past the metals.
Abiding-Pressure Calorimetry
A abiding-pressure calorimeter measures the modify in enthalpy of a reaction occurring in solution during which the atmospheric pressure remains constant. An case is a coffee-cup calorimeter, which is constructed from ii nested Styrofoam cups and a hat with ii holes, assuasive insertion of a thermometer and a stirring rod. The inner cup holds a known amount of a solute, usually water, that absorbs the heat from the reaction. When the reaction occurs, the outer cup provides insulation. And so
[latex]\text{C}_{\text{P}}=\frac{\text{W}\Delta \text{H}}{\text{M}\Delta \text{T}}[/latex]
where Cp is the specific heat at constant pressure level, ΔH is the enthalpy of the solution, ΔT is the change in temperature, West is the mass of the solute, and M is the molecular mass of the solute. The measurement of estrus using a simple calorimeter, similar the java cup calorimeter, is an instance of constant-pressure calorimetry, since the force per unit area (atmospheric pressure) remains abiding during the process. Constant-pressure calorimetry is used in determining the changes in enthalpy occurring in solution. Under these conditions the change in enthalpy equals the heat (Q=ΔH).
Specific Rut for an Ideal Gas at Constant Pressure and Volume
An ideal gas has different specific heat capacities nether constant volume or constant pressure weather.
Learning Objectives
Explain how to derive the adiabatic index
Key Takeaways
Key Points
- The specific heat at constant volume for a gas is given as [latex](\frac{\partial \text{U}}{\partial \text{T}})_{\text{V}}=\text{c}_{\text{5}}[/latex].
- The specific rut at abiding pressure for an ideal gas is given as [latex](\frac{\partial \text{H}}{\partial \text{T}})_{\text{Five}}=\text{c}_{\text{p}}=\text{c}_{\text{v}}+\text{R}[/latex].
- The heat capacity ratio (or adiabatic index ) is the ratio of the heat chapters at abiding pressure to heat capacity at constant volume.
Cardinal Terms
- Fundamental Thermodynamic Relation: In thermodynamics, the cardinal thermodynamic relation expresses an infinitesimal modify in internal free energy in terms of minute changes in entropy, and book for a closed organisation in thermal equilibrium in the following way: dU=TdS-PdV. Here, U is internal energy, T is absolute temperature, Due south is entropy, P is pressure and 5 is volume.
- adiabatic index: The ratio of the oestrus capacity at constant pressure to heat capacity at constant volume.
- specific heat: The ratio of the corporeality of heat needed to raise the temperature of a unit of measurement mass of substance by a unit degree to the amount of oestrus needed to enhance that of the same mass of water by the same amount.
Specific Estrus for an Ideal Gas at Abiding Pressure and Volume
The heat capacity at abiding volume of nR = one J·1000−1 of any gas, including an ideal gas is:
[latex](\frac{\partial \text{U}}{\partial \text{T}})_{\text{V}}=\text{c}_{\text{v}}[/latex]
This represents the dimensionless rut chapters at abiding volume; it is generally a function of temperature due to intermolecular forces. For moderate temperatures, the abiding for a monoatomic gas is cv=3/two while for a diatomic gas it is cfive=5/2 (see ). Macroscopic measurements on heat chapters provide data on the microscopic structure of the molecules.
Molecular internal vibrations: When a gas is heated, translational kientic energy of molecules in the gas volition increase. In add-on, molecules in the gas may pick up many feature internal vibrations. Potential energy stored in these internal degrees of freedom contributes to specific heat of the gas.
The rut capacity at constant pressure of 1 J·Thousand−1 ideal gas is:
[latex](\frac{\partial \text{H}}{\partial \text{T}})_{\text{V}}=\text{c}_{\text{p}}=\text{c}_{\text{five}}+\text{R}[/latex]
where H=U+pV is the enthalpy of the gas.
Measuring the heat capacity at constant volume can be prohibitively hard for liquids and solids. That is, small-scale temperature changes typically require large pressures to maintain a liquid or solid at constant volume (this implies the containing vessel must exist nearly rigid or at to the lowest degree very strong). It is easier to measure the heat capacity at constant pressure level (allowing the cloth to expand or contract freely) and solve for the rut capacity at constant volume using mathematical relationships derived from the basic thermodynamic laws.
Utilizing the Fundamental Thermodynamic Relation we tin can show:
[latex]\text{C}_{\text{p}}-\text{C}_{\text{V}}=\text{T}(\frac{\partial \text{P}}{\partial \text{T}})_{\text{V},\text{N}}(\frac{\partial \text{5}}{\fractional \text{T}})_{\text{p},\text{N}}[/latex]
where the partial derivatives are taken at: constant volume and constant number of particles, and at constant pressure and constant number of particles, respectively.
The heat capacity ratio or adiabatic index is the ratio of the oestrus capacity at abiding pressure to oestrus chapters at abiding volume. It is sometimes besides known as the isentropic expansion cistron:
[latex]\gamma =\frac{\text{C}_{\text{P}}}{\text{C}_{\text{V}}}=\frac{\text{c}_{\text{p}}}{\text{c}_{\text{v}}}[/latex]
For an ideal gas, evaluating the fractional derivatives to a higher place according to the equation of state, where R is the gas constant for an ideal gas yields:
[latex]\text{pV} = \text{RT}[/latex]
[latex]\text{C}_{\text{p}}-\text{C}_{\text{Five}}=\text{T}(\frac{\partial \text{P}}{\partial \text{T}})_{\text{V}}(\frac{\fractional \text{V}}{\partial \text{T}})_{\text{p}}[/latex]
[latex]\text{C}_{\text{p}}-\text{C}_{\text{5}}=-\text{T}(\frac{\fractional \text{P}}{\partial \text{V}})_{\text{V}}(\frac{\partial \text{V}}{\partial \text{T}})_{\text{p}}^{2}[/latex]
[latex]\text{P}=\frac{\text{RT}}{\text{V}}\text{northward} \to (\frac{\partial \text{P}}{\partial \text{Five}})_{\text{T}}=\frac{-\text{RT}}{\text{Five}^{2}}=\frac{-\text{P}}{\text{Five}}[/latex]
[latex]\text{V}=\frac{\text{RT}}{\text{P}}\text{n} \to (\frac{\partial \text{V}}{\partial \text{T}})^{ii}_{\text{p}}=\frac{\text{R}^{2}}{\text{P}^{2}}[/latex]
substituting:
[latex]-\text{T}(\frac{\fractional \text{P}}{\fractional \text{V}})_{\text{V}}(\frac{\partial \text{V}}{\partial \text{T}})_{\text{p}}^{two}=-\text{T}\frac{-\text{P}}{\text{V}}\frac{\text{R}^{2}}{\text{P}^{2}}=\text{R}[/latex]
This equation reduces only to what is known every bit Mayer'south relation:
Julius Robert Mayer: Julius Robert von Mayer (November 25, 1814 – March 20, 1878), a High german physician and physicist, was one of the founders of thermodynamics. He is best known for his 1841 enunciation of one of the original statements of the conservation of energy (or what is now known as ane of the first versions of the first law of thermodynamics): "Energy tin can be neither created nor destroyed. " In 1842, Mayer described the vital chemic process now referred to as oxidation as the primary source of free energy for whatsoever living creature. His achievements were disregarded and credit for the discovery of the mechanical equivalent of heat was attributed to James Joule in the following year. von Mayer also proposed that plants convert light into chemic free energy.
[latex]\text{C}_{\text{P}}-\text{C}_{\text{V}}=\text{R}[/latex].
It is a uncomplicated equation relating the heat capacities nether constant temperature and under abiding pressure.
Solving Issues with Calorimetry
Calorimetry is used to measure out the corporeality of rut produced or consumed in a chemic reaction.
Learning Objectives
Explain a bomb calorimeter is used to mensurate heat evolved in a combustion reaction
Key Takeaways
Cardinal Points
- Calorimetry is used to measure amounts of heat transferred to or from a substance.
- A calorimeter is a device used to measure the amount of heat involved in a chemical or physical procedure.
- This ways that the corporeality of heat produced or consumed in the reaction equals the amount of heat absorbed or lost past the solution.
Key Terms
- heat of reaction: The enthalpy modify in a chemic reaction; the amount of estrus that a systems gives up to its surroundings so it tin render to its initial temperature.
- combustion: A process where two chemicals are combined to produce heat.
Calorimeters are designed to minimize free energy exchange between the system being studied and its surroundings. They range from simple coffee cup calorimeters used past introductory chemical science students to sophisticated flop calorimeters used to determine the energy content of food.
Calorimetry is used to measure amounts of estrus transferred to or from a substance. To practice and so, the oestrus is exchanged with a calibrated object (calorimeter). The alter in temperature of the measuring part of the calorimeter is converted into the amount of heat (since the previous calibration was used to found its heat chapters ). The measurement of heat transfer using this approach requires the definition of a system (the substance or substances undergoing the chemical or physical alter) and its surroundings (the other components of the measurement apparatus that serve to either provide heat to the organisation or absorb heat from the system). Knowledge of the heat chapters of the surroundings, and careful measurements of the masses of the system and surroundings and their temperatures before and later on the process allows one to summate the estrus transferred as described in this section.
A calorimeter is a device used to measure the amount of heat involved in a chemical or concrete process. For case, when an exothermic reaction occurs in solution in a calorimeter, the rut produced past the reaction is captivated by the solution, which increases its temperature. When an endothermic reaction occurs, the rut required is absorbed from the thermal energy of the solution, which decreases its temperature. The temperature change, forth with the specific estrus and mass of the solution, can then be used to summate the amount of heat involved in either case.
Coffee-Loving cup Calorimeters
General chemistry students often use uncomplicated calorimeters synthetic from polystyrene cups. These easy-to-use "coffee loving cup" calorimeters allow more rut substitution with their environs, and therefore produce less accurate energy values.
Structure of the Constant Volume (or "Bomb") Calorimeter
Flop Calorimeter: This is the picture of a typical setup of bomb calorimeter.
A unlike type of calorimeter that operates at constant book, colloquially known as a bomb calorimeter, is used to measure the energy produced by reactions that yield large amounts of heat and gaseous products, such equally combustion reactions. (The term "flop" comes from the observation that these reactions can be vigorous enough to resemble explosions that would harm other calorimeters.) This type of calorimeter consists of a robust steel container (the "bomb") that contains the reactants and is itself submerged in water. The sample is placed in the bomb, which is and so filled with oxygen at high pressure level. A pocket-size electric spark is used to ignite the sample. The free energy produced by the reaction is trapped in the steel bomb and the surrounding h2o. The temperature increase is measured and, along with the known estrus capacity of the calorimeter, is used to summate the energy produced by the reaction. Flop calorimeters crave scale to decide the rut capacity of the calorimeter and ensure accurate results. The calibration is accomplished using a reaction with a known q, such equally a measured quantity of benzoic acrid ignited by a spark from a nickel fuse wire that is weighed before and after the reaction. The temperature change produced by the known reaction is used to determine the oestrus capacity of the calorimeter. The calibration is by and large performed each time before the calorimeter is used to gather research data.
Example: Identifying a Metal by Measuring Specific Estrus
A 59.7 g piece of metallic that had been submerged in boiling water was quickly transferred into lx.0 mL of h2o initially at 22.0 °C. The final temperature is 28.5 °C. Use these data to make up one's mind the specific estrus of the metal. Apply this upshot to place the metal.
Solution
Assuming perfect estrus transfer, the oestrus given off by metal is the negative of the oestrus taken in past water, or:
[latex]\text{q}_{\text{metal}}=-\text{q}_{\text{h2o}}[/latex]
In expanded grade, this is:
[latex]\text{c}_{\text{metal}} \times \text{yard}_{\text{metal}} \times \left( \text{T}_{\text{f,metal}}-\text{T}_{\text{i,metal}} \right) = \text{c}_{\text{water}} \times \text{m}_{\text{water}} \times \left( \text{T}_{\text{f,water}}-\text{T}_{\text{i,h2o}} \right)[/latex]
Noting that since the metal was submerged in boiling water, its initial temperature was 100.0 °C; and that for water, 60.0 mL = 60.0 yard; we take:
[latex]\left( \text{c}_{\text{metal}} \right)\left( 59.7\text{ g} \right)\left( 28.v^{\text{o}} \text{C} - 100.0^{\text{o}} \text{C} \correct) = \left( four.xviii \text{ J/chiliad}^{\text{o}} \text{C} \correct) \left( 60.0\text{ k} \right)\left( 28.v^{\text{o}} \text{C} - 22.0^{\text{o}} \text{C} \correct)[/latex]
Solving this:
[latex]\text{c}_{\text{metal}} = \dfrac{- \left( four.184 \text{ J/g}^{\text{o}} \text{C} \right) \left( 60.0\text{ one thousand} \right)\left( 6.v^{\text{o}} \text{C} \right)}{\left( 59.7\text{ g} \right)\left( -71.5^{\text{o}} \text{C} \right)} = 0.38 \text{ J/yard}^{\text{o}} \text{C} [/latex]
Our experimental specific estrus is closest to the value for copper (0.39 J/k °C), and so nosotros identify the metal as copper.
Source: https://courses.lumenlearning.com/boundless-physics/chapter/specific-heat/
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