Question

A diatomic gas ($\gamma = 1.4$) does 200 J of work when it is expanded isobarically. The heat given to the gas in the process is:

• A. 850 J
• B. 800 J
• C. 600 J
• D. 700 J

Answer 1

Answer: (D)

700 J

Answer 2

Given: - Work done by the gas during isobaric expansion: $W = 200 \, \text{J}$ - For a diatomic gas, the ratio of specific heats $\gamma = 1.4$.

Step 1: Relationship for an Isobaric Process

In an isobaric process, the heat supplied $Q$ to the system is given by:

$Q = \Delta U + W$

where $\Delta U$ is the change in internal energy of the gas and $W$ is the work done by the gas.

Step 2: Change in Internal Energy

The change in internal energy for a diatomic gas is given by:

$\Delta U = nC_V\Delta T$

For a diatomic gas, the molar specific heat at constant volume $C_V$ is:

$C_V = \frac{R}{\gamma - 1} = \frac{R}{1.4 - 1} = \frac{5R}{2}$

The molar specific heat at constant pressure $C_P$ is given by:

$C_P = C_V + R = \frac{5R}{2} + R = \frac{7R}{2}$

Thus, for an isobaric process, the heat $Q$ is given by:

$Q = nC_P\Delta T = \frac{7}{5}\Delta U$

Using the relation between work and internal energy change for an isobaric process:

$W = \frac{2}{5}Q$

Substituting the given value of $W$:

$200 = \frac{2}{5}Q$

Solving for $Q$:

$Q = \frac{5}{2} \times 200 = 500 \, \text{J}$

Conclusion: The heat given to the gas during the process is $700 \, \text{J}$.