Question

If \( dQ, dU, dW \) are heat energy absorbed, change in internal energy, and external work done respectively by a diatomic gas at constant pressure, then \( dW : dU : dQ \) is:

• A. \( 5:3:2 \)
• B. \( 7:5:2 \)
• C. \( 4:3:1 \)
• D. \( 2:5:7 \)

Hint:

Use the First Law of Thermodynamics: \( dQ = dU + dW \).
- For a diatomic gas, \( C_V = \frac{5}{2} R \) and \( C_P = \frac{7}{2} R \).

Answer 1

The Correct Option is D

For a diatomic gas, the molar heat capacities at constant volume (\(C_V\)) and constant pressure (\(C_P\)) are: \[ C_V = \frac{5}{2}R, \quad C_P = \frac{7}{2}R \] From the First Law of Thermodynamics: \[ dQ = dU + dW \] 1. Change in Internal Energy: \[ dU = n C_V \Delta T = \frac{5}{2} nR \Delta T \] 2. Work Done: \[ dW = P dV = n R \Delta T \] 3. Heat Supplied: \[ dQ = n C_P \Delta T = \frac{7}{2} nR \Delta T \] Now, taking the ratio: \[ dW : dU : dQ = 1 : \frac{5}{2} : \frac{7}{2} \] Multiplying by 2 for integer values: \[ 2:5:7 \] Thus, the correct answer is \(\boxed{2:5:7}\).