Question

A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in increasing the internal energy and that used for doing external work is $A$ and $B$ respectively. Then the ratio, $\text{A} : \text{B}$ is

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

Hint:

For monoatomic gases at constant $P$, 60% of heat goes to internal energy and 40% to work.

Answer 1

The Correct Option is C

Step 1: Concept
For constant pressure process, $Q = \Delta U + W$. For monoatomic gas, $\Delta U = \frac{3}{2} nR\Delta T$ and $Q = \frac{5}{2} nR\Delta T$.

Step 2: Meaning
$W = Q - \Delta U = \frac{5}{2} nR\Delta T - \frac{3}{2} nR\Delta T = nR\Delta T$.

Step 3: Analysis
Percentage A ($\Delta U$) $\propto 3/2$ and Percentage B ($W$) $\propto 1$.
Ratio $A:B = \frac{3}{2} : 1 = 3 : 2$.

Step 4: Conclusion
The ratio is $3:2$. Final Answer: (C)