Question:medium
When an ideal gas $(\gamma = \frac{5}{3})$ is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work?
When an ideal gas $(\gamma = \frac{5}{3})$ is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work?
Show Hint
For heating at constant pressure:
\[
\frac{W}{Q}=\frac{R}{C_P}
\]
So first find \(C_P\) from \(\gamma\), then directly calculate the fraction.
Updated On: May 14, 2026
- $60%$
- $20%$
- $30%$
- $40%$
Show Solution
The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
For constant pressure expansion, heat supplied is shared between increasing internal energy and doing work.
Step 2: Key Formula or Approach:
Fraction of work $= \Delta W / \Delta Q = (\gamma - 1) / \gamma$.
Step 3: Detailed Explanation:
$\gamma = 5/3$. Fraction $= (5/3 - 1) / (5/3) = (2/3) / (5/3) = 2/5 = 0.4$.
Percentage $= 0.4 \times 100 = 40%$.
Step 4: Final Answer:
The percentage is $40%$.
For constant pressure expansion, heat supplied is shared between increasing internal energy and doing work.
Step 2: Key Formula or Approach:
Fraction of work $= \Delta W / \Delta Q = (\gamma - 1) / \gamma$.
Step 3: Detailed Explanation:
$\gamma = 5/3$. Fraction $= (5/3 - 1) / (5/3) = (2/3) / (5/3) = 2/5 = 0.4$.
Percentage $= 0.4 \times 100 = 40%$.
Step 4: Final Answer:
The percentage is $40%$.
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