Question

When 80 J of heat is supplied to a gas at constant pressure, if the work done by the gas is 20 J, then the ratio of the specific heat capacities of the gas is

• A. 4/3
• B. 5/3
• C. 7/5
• D. 9/7

Hint:

$C_p - C_v = R$. At constant pressure, $Q = nC_p\Delta T$ and $W = nR\Delta T$.

Answer 1

The Correct Option is A

At constant pressure, the heat supplied $Q = nC_p\Delta T$, where $n$ is the number of moles, $C_p$ is the specific heat at constant pressure, and $\Delta T$ is the change in temperature. Work done by the gas $W = P\Delta V = nR\Delta T$, where $R$ is the ideal gas constant. We are given $Q = 80$ J and $W = 20$ J. $80 = nC_p\Delta T$ $20 = nR\Delta T$ Dividing the first equation by the second: $\frac{80}{20} = \frac{C_p}{R}$ $C_p = 4R$. We know that $C_p - C_v = R$, where $C_v$ is the specific heat at constant volume. $4R - C_v = R$ $C_v = 3R$. The ratio of specific heats is $\frac{C_p}{C_v} = \frac{4R}{3R} = \frac{4}{3}$.