Question:
Certain quantity of heat is supplied to a monoatomic ideal gas which expands at constant pressure. The percentage of heat that goes into work done by the gas is
Certain quantity of heat is supplied to a monoatomic ideal gas which expands at constant pressure. The percentage of heat that goes into work done by the gas is
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For monoatomic gas: 40% work, 60% internal energy. For diatomic gas: $\approx$ 28% work, 72% internal energy.
Updated On: Jul 4, 2026
- 20%
- 40%
- 60%
- 80%
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The Correct Option is B
Solution and Explanation
Step 1: Concept
For an ideal gas at constant pressure, heat supplied $Q = nC_{p}dT$ and work done $W = nRdT$.
Step 2: Meaning
The ratio of work done to heat supplied is $W/Q = \frac{nRdT}{nC_{p}dT} = \frac{R}{C_{p}}$.
Step 3: Analysis
For a monoatomic gas, $C_{v} = \frac{3}{2}R$ and $C_{p} = C_{v} + R = \frac{5}{2}R$. The ratio is $R / (\frac{5}{2}R) = 2/5$.
Step 4: Conclusion
Percentage of work = $(2/5) \times 100 = 40\%$. Final Answer: (B)
For an ideal gas at constant pressure, heat supplied $Q = nC_{p}dT$ and work done $W = nRdT$.
Step 2: Meaning
The ratio of work done to heat supplied is $W/Q = \frac{nRdT}{nC_{p}dT} = \frac{R}{C_{p}}$.
Step 3: Analysis
For a monoatomic gas, $C_{v} = \frac{3}{2}R$ and $C_{p} = C_{v} + R = \frac{5}{2}R$. The ratio is $R / (\frac{5}{2}R) = 2/5$.
Step 4: Conclusion
Percentage of work = $(2/5) \times 100 = 40\%$. Final Answer: (B)
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