Question

A piece of lead [c = 128 J/(kg·C°)] is heated from 18.0 °C to 30.1 °C. The same amount of heat is added to a piece of copper [c = 387 J/(kg·C°)]. The mass and initial temperature of the copper are the same as for the lead. Determine the final temperature Tf of the copper.

Answer 1

Answer on Question#37931, Physics, Other

Question:

A piece of lead [c = 128 J/(kg·C°)] is heated from 18.0 °C to 30.1 °C. The same amount of heat is added to a piece of copper [c = 387 J/(kg·C°)]. The mass and initial temperature of the copper are the same as for the lead. Determine the final temperature Tf of the copper.

Answer:

The amount of heat which is needed to add to the body to increase its temperature from $T_0$ to $T_f$ is

$$Q = c m (T_f - T_0)$$

where c - is specific heat of the body, m - mass of the body.

The amount of heat is added to the piece of lead and to the piece of copper is the same, so we can write an equation

$$c_l m (T_{fl} - T_0) = c_c m (T_{fc} - T_0)$$

So we can find the final temperature $T_{fc}$ of the copper

$$T_{fc} = T_0 + \frac{c_l}{c_c} (T_{fl} - T_0)$$ $$T_{fc} = 18.0 + \frac{128}{387} (30.1 - 18.0) = 22.0{}^{\circ}\mathrm{C}$$

The answer is: $T_{fc} = 22.0{}^{\circ}\mathrm{C}$