Question

A sample of ideal gas $(\gamma =1.4)$ is heated at constant pressure. If an amount of $100J$ heat is supplied to the gas, the work done by the gas is

• A. $28.57J$
• B. $56.28J$
• C. $36.23J$
• D. $42.12J$

Answer 1

Answer: (A)

$28.57J$

Given,

$\gamma =1.4$

$\Delta Q=100J$

For ideal gas,

Change in heat,

$\Delta Q=n{C}_P(T_2-T_1)$. . . . . . . . .(1)

Change in internal energy,

$\Delta U=n{C}_V(T_2-T_1)$. . . . . . .. . . . .(2)

Divide equation (2) by equation (1), we get

$\frac{\Delta U}{\Delta Q}=\frac{n{C}_V(T_2-T_1)}{n{C}_P(T_2-T_1)}=\frac{C_V}{C_P}$

$\Delta U=\frac{\Delta Q}{\gamma }$

$\Delta U=\frac{100}{1.4}=71.42J$

From first law of thermodynamics,

$\Delta Q=\Delta U+\Delta W$

$\Delta W=\Delta Q-\Delta U$

$\Delta W=100-71.42$

$\Delta W=28.57J$

The correct option is A.