A metal brick found in an excavation was sent to a testing...

A metal brick found in an excavation was sent to a testing lab for nondestructive identification. The lab weighed the sample brick and found its mass to be $3.0 \mathrm{~kg} .$ The brick was heated to a temperature of $3.0 \cdot 10^{2}{ }^{\circ} \mathrm{C}$ and dropped into an insulated copper calorimeter of mass 1.5 kg containing $2.0 \mathrm{~kg}$ of water at $2.0 \cdot 10^{1}{ }^{\circ} \mathrm{C} .$ The final temperature at equilibrium was noted to be $31.7^{\circ} \mathrm{C}$. By calculating the specific heat of the sample from this data, can you identify the brick's material?

Key Concepts

Thermal Equilibrium

Thermal equilibrium is achieved when two or more objects in thermal contact no longer exchange heat, meaning they have reached the same temperature. In calorimetry, reaching thermal equilibrium allows for the direct comparison of the heat content of different parts of the system. It is an essential concept in determining heat capacities and understanding the distribution of thermal energy within the system.

Calorimetry

Calorimetry is the process of measuring the amount of heat exchanged in physical or chemical processes. In experiments like this, a heated object is submerged in a cooler medium contained in an insulated calorimeter, and the resulting change in temperature of the system is used to calculate the heat transferred. This principle is crucial for determining properties such as the specific heat capacity of materials.

Specific Heat Capacity

Specific heat capacity is a material property that indicates the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. It is a fundamental parameter used to characterize materials, and, when determined experimentally through calorimetry, can help in identifying unknown substances by comparing the measured value to known standards.

Conservation of Energy in Heat Transfer

The principle of conservation of energy states that energy cannot be created or destroyed, only transferred. In the context of this experiment, the heat lost by the heated metal brick is assumed to be equal to the heat gained by the water and the calorimeter. This assumption allows for the calculation of the metal's specific heat when the changes in temperature are measured, providing a basis for material identification.

Transcript

00:01 You can say that the heat lost by the metal, the unknown metal, q sub m, would be equaling to the mass of the metal, multiplied by the specific heat capacity of the metal, multiplied by the equilibrium temperature minus the initial temperature of the metal.

00:17 We can say that the heat gained by the water and the copper calorimeter would be equaling then to the mass of copper times the specific heat of copper.

00:33 T minus the initial temperature of the copper calorimeter plus the mass of the water times the specific heat capacity of the water multiplied by the equilibrium temperature minus the initial temperature of the water.

00:47 And so we can then say that q sub m plus q sub copper plus q sub water should equal zero and we get that m sub m c sub m multiplied by t minus t sub m.

01:12 This would be plus the mass of the copper, c sub copper, t minus the initial temperature of the copper, plus mass of water, c sub water, t minus temperature, the initial temperature of the water, equaling zero.

01:33 And then we can essentially solve, and we know that the temperature of the copper, the initial temperature of the copper is equal to the initial temperature of the water.

01:51 And so we can then solve for the specific heat capacity of the metal.

01:55 And this would be the negative mass of copper, heat capacity of copper, plus the mass of water times the heat capacity of water, multiplied by t minus the initial temperature of the water or the initial temperature of the copper.

02:13 It doesn't matter.

02:16 Divided by the mass of the metal, multiplied by the equilibrium temperature minus the initial temperature of the metal...

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