Question

A diatomic gas, having $C_p = \frac{7}{2}R$ and $C_v = \frac{5}{2}R$, is heated at constant pressure. The ratio $dU : dQ : dW$:

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

Hint:

For any ideal gas at constant pressure: - $dU/dQ = 1/\gamma$ - $dW/dQ = 1 - 1/\gamma$ For diatomic gas, $\gamma = 7/5$.

Answer 1

The Correct Option is A

Step 1: $dQ = n C_p dT = n (\frac{7}{2}R) dT$.
Step 2: $dU = n C_v dT = n (\frac{5}{2}R) dT$.
Step 3: $dW = dQ - dU = n (C_p - C_v) dT = nRdT$.
Step 4: Ratio $dU : dQ : dW = \frac{5}{2} : \frac{7}{2} : 1 = 5 : 7 : 2$.