1.0 mol of an elemental solid and 1.0 mol of a monatomic gas interact thermally.What is the temperature change of the solid if the gas temperature decreases by 60°C at constant volume?
A)30°C increase
B)30°C decrease
C)60°C increase
D)60°C decrease

Question

Quizplus · Accepted Answer

According to the Law of Dulong and Petit, the molar heat capacity of an elemental solid is around 3R, where R is the gas constant. This means that the elemental solid requires 3 times more energy to increase its temperature by 1°C compared to a monatomic gas (with a molar heat capacity of 3/2 R).

When the gas temperature decreases by 60°C, the energy lost by the gas is gained by the solid, assuming no energy is lost to the surroundings. Since the gas has a 3/2 R heat capacity and there is 1 mol of gas, the energy lost is -3/2 R * 1 mol * 60°C = -270 J.

To gain this amount of energy, the solid needs to increase its temperature by (270 J)/(3R * 1 mol) = 30°C (using the fact that 1 mol of the solid is present). Therefore, the temperature of the solid increases by 30°C, which is choice A.

10 Mol of an Elemental Solid and 1