Question

Heat is supplied to a rigid diatomic gas at constant pressure. The ratio of \(\Delta Q:\Delta U:\Delta W\) is \(\{\Delta Q=\text{heat supplied},\Delta U=\text{change in internal energy},\Delta W=\text{work done during expansion}\}\)

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

Hint:

At constant pressure the heat, internal energy change and work are in the ratio of the molar heat capacities \(C_{p}:C_{v}:R\).

Answer 1

The Correct Option is C

Step 1: First law
$\Delta Q=\Delta U+\Delta W$, and $\Delta W=nR\Delta T$ at constant pressure.

Step 2: Use the degrees of freedom
With 5 degrees of freedom $\Delta U=\frac{5}{2}nR\Delta T$, so $\Delta Q=\frac{5}{2}+1=\frac{7}{2}$ in units of $nR\Delta T$.

Step 3: Ratio
$\frac{7}{2}:\frac{5}{2}:1=7:5:2$, option (C).

Final Answer:
The ratio of the three quantities is 7 : 5 : 2. \[ \boxed{\text{(C) }7:5:2} \]