Heat Capacity and Calorimetry Question 4

A 10. g cube of copper at a temperature $T_1$ is placed in an insulated cup containing 10. g of water at a temperature $T_2$ . If $T_1 \gt T_2$ , which of the following is true of the system when it has attained thermal equilibrium? (The specific heat of copper is $\pu{0.385 J/(g}\cdot^\circ$ C) and the specific heat of water is $\pu{4.18 J/(g}\cdot^\circ$ C).)

The temperature of the copper changed more than the temperature of the water.

The temperature of the water changed more than the temperature of the copper.

The temperature of the water and the copper changed by the same amount.

The relative temperature changes of the copper and the water cannot be determined without knowing

T_1

and

T_2

Approach

The question mentions that the initial temperature of copper is greater ( $T_1 \gt T_2$ ). This implies that the copper will transfer heat to the water. Since copper has a lower specific heat, less energy is required to change the temperature of copper. Because both the copper and water have equal masses, the temperature of copper must have decreased much more than the increase in temperature of the water.

q_{\text{lost by copper}} = -q_{\text{gained by water}}

mc\Delta T = mc\Delta T

(10)(0.385)(T_1-T_f) = -(10)(4.18)(T_f-T_2)

(0.385)(\Delta T_{\text{copper}}) = (4.18)(\Delta T_{\text{water}})

\Delta T_{\text{copper}} \gg \Delta T_{\text{water}}