Physics · Heat and Thermodynamics | MDCAT MCQ

Question

An ideal gas has molar specific heat Cp at constant pressure. When the temperature of n moles is increased by AT the increase in the internal energy is:

Options

A
nCp △T
B
n(Cp + R) △T
C
n(Cp - R) △T
D
n(2Cp + R) △T

Explanation

This is the correct option. It represents the increase in internal energy of an ideal gas when the temperature is increased by ΔT\Delta TΔT. In this equation, nnn is the number of moles, CpC_pCp is the molar specific heat at constant pressure, and RRR is the ideal gas constant. The term (Cp−R)(C_p - R)(Cp−R) reflects the relationship between the specific heats at constant pressure and constant volume. This option shows how internal energy is dependent on the change in temperature and the difference between the specific heats.

This option is incorrect in the context of calculating the increase in internal energy for an ideal gas. While this expression calculates the heat added at constant pressure, it does not represent the change in internal energy, as it does not account for the work done by the gas when it expands.

This option suggests that the increase in internal energy includes both the molar specific heat at constant pressure (Cp) and the gas constant (R). It implies that the gas is not ideal.

This is the correct option. It represents the increase in internal energy of an ideal gas when the temperature is increased by ΔT\Delta TΔT. In this equation, nnn is the number of moles, CpC_pCp is the molar specific heat at constant pressure, and RRR is the ideal gas constant. The term (Cp−R)(C_p - R)(Cp−R) reflects the relationship between the specific heats at constant pressure and constant volume. This option shows how internal energy is dependent on the change in temperature and the difference between the specific heats.

This option suggests that the increase in internal energy includes twice the molar specific heat at constant pressure (2Cp) and the gas constant (R). It also implies that the gas is not ideal.