Question

Heat is applied to a rigid diatomic gas at constant pressure. The ratio \( \Delta Q : \Delta U : \Delta W \) is

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

Hint:

For constant pressure processes, always remember \( C_p = C_v + R \).

Answer 1

The Correct Option is B

Step 1: Degrees of freedom of diatomic gas.
For a rigid diatomic gas, degrees of freedom \[ f = 5 \]
Step 2: Write expressions for thermodynamic quantities.
At constant pressure, \[ \Delta Q = n C_p \Delta T \] \[ \Delta U = n C_v \Delta T \] \[ \Delta W = n R \Delta T \]
Step 3: Use values of \( C_p \) and \( C_v \).
\[ C_v = \frac{f}{2} R = \frac{5}{2} R \] \[ C_p = C_v + R = \frac{7}{2} R \]
Step 4: Write ratio.
\[ \Delta Q : \Delta U : \Delta W = \frac{7}{2}R : \frac{5}{2}R : R \]
Step 5: Simplify ratio.
\[ 7 : 5 : 2 \]
Step 6: Conclusion.
The correct ratio is \( 7 : 5 : 2 \).