Answer to Question #99975 in Molecular Physics | Thermodynamics for don

Question

A 10 kg lead brick is dropped from a height of 60 meters. If the energy change is converted to heat, how much the does the temperature of the brick change? The specific heat capacity of lead is 130 J/(kg C). Assume all the heat goes into the brick.

For full credit, give the equation that relates the relevant data to the answer and show the given values substituted into the equation to solve for the answer. Put proper units with all numbers.

Answer 1

The amount of heat transferred to the brick is equal to change of its mechanical energy.

$$Q=\Delta E$$

$$cm\Delta T=mgh$$

So, the change of the brick temperature

$$\Delta T=\frac{gh}{c}$$

$$\Delta T=\frac{9.8\:\rm m/s^2\times 60\: m}{130\:\rm J/(kg\cdot C^{\circ})}=4.52\:\rm C^{\circ}$$