Question

A diatomic gas, having ${\mathrm{C}}_{\mathrm{P}}=(7/2)\mathrm{R}$ and ${\mathrm{C}}_{\mathrm{v}}=(5/2)\mathrm{R},$ is heated at constant pressure. The ratio $\mathrm{dU}:\mathrm{dQ}:\mathrm{dW}$

• A. .$3:7:2$
• B. $5:7:2$
• C. $5:7:3$
• D. $3:5:2$

Answer 1

The correct option is B

$5:7:2$

Answer:(B)

Explanation for correct option:

Step 1: Given data

$$\begin{gathered} {\mathrm{C}}_{\mathrm{p}}=(7/2)\mathrm{R} \\ {\mathrm{C}}_{\mathrm{V}}=(5/2)\mathrm{R} \end{gathered}$$

Step 2: To calculate $\mathrm{dU}$, $\mathrm{dQ}$and $\mathrm{dW}$

Since the gas is diatomic in nature and the process is isobaric in nature, we use the formula:

$$\begin{gathered} \mathrm{dU}={\mathrm{nC}}_{\mathrm{V}}\mathrm{dT} \\ \mathrm{dQ}={\mathrm{nC}}_{\mathrm{p}}\mathrm{dT} \\ \mathrm{dW}=\mathrm{P}\times \mathrm{dV} \\ \mathrm{dW}=\mathrm{nRdT} \end{gathered}$$

Step 3: To calculate $\mathrm{dU}:\mathrm{dQ}:\mathrm{dW}$

$$\begin{gathered} \mathrm{dU}:\mathrm{dQ}:\mathrm{dW} \\ {\mathrm{C}}_{\mathrm{V}}:{\mathrm{C}}_{\mathrm{p}}:\mathrm{R} \\ (5/2)\mathrm{R}:(7/2)\mathrm{R}:\mathrm{R} \\ 5:7:2 \end{gathered}$$

Hence option (B) is correct option.