Question

A sample of an ideal gas ($\gamma = 5/3$) is heated at constant pressure. If 100 J of heat is supplied to the gas, the work done by the gas is ______.

• A. 150 J
• B. 60 J
• C. 40 J
• D. 250 J

Hint:

Memorize the energy distribution ratios for isobaric heating of a monoatomic gas ($\gamma = 5/3$):
$\Delta U : W : Q \implies 3 : 2 : 5$.
If $Q = 100$, then $W = 40$ and $\Delta U = 60$. It solves the problem in 2 seconds!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
At constant pressure (isobaric process), the heat supplied ($dQ$), change in internal energy ($dU$), and work done ($dW$) are related to the degrees of freedom and $\gamma$.

Step 2: Formula Application:
For an isobaric process: $dW/dQ = (C_p - C_v)/C_p = 1 - (1/\gamma)$.

Step 3: Explanation:
Given $dQ = 100$ J and $\gamma = 5/3$. $dW = dQ \left( 1 - \frac{1}{5/3} \right) = 100 \left( 1 - \frac{3}{5} \right)$ $dW = 100 \left( \frac{2}{5} \right) = 40$ J.

Step 4: Final Answer:
The work done by the gas is 40 J.