Free Molar Specific Heat of a Gas MCQs with Answers

1. For a gas, the molar specific heat at constant pressure Cp is greater than that at constant volume Cv because

• A. the gas is hotter at constant pressure
• B. at constant pressure the gas also does work expanding against the surroundings
• C. the molecules move faster at constant pressure
• D. Cv is measured at a lower temperature

Explanation: At constant volume all the heat supplied raises the internal energy, but at constant pressure some of it is spent doing work as the gas expands, so more heat is needed for the same temperature rise. The difference is exactly the gas constant R, which is Mayer's relation. This is why Cp always exceeds Cv for any gas.

2. The relation between the two molar specific heats of an ideal gas is

• A. Cp minus Cv equals R
• B. Cp plus Cv equals R
• C. Cp times Cv equals R
• D. Cp equals Cv

Explanation: Mayer's relation follows directly from the first law applied to a constant pressure heating, where the extra heat needed is the work of expansion, which for one mole and a one kelvin rise is R. The ratio Cp over Cv, written gamma, is about 1.67 for a monatomic gas and 1.4 for a diatomic one. Gamma governs the speed of sound and adiabatic changes.

3. According to the kinetic theory, the absolute temperature of a gas is directly proportional to

• A. the average speed of its molecules
• B. the average kinetic energy of its molecules
• C. the number of molecules present
• D. the volume of the container

Explanation: Average translational kinetic energy per molecule is three halves kT, so it is the energy rather than the speed that is proportional to temperature. Since energy depends on the square of the speed, doubling the absolute temperature raises the root mean square speed only by the square root of two. This distinction is the point of the question.