Question

A diatomic gas (\( \gamma = 1.4 \)) does 100 J of work in an isobaric expansion. The heat given to the gas is:

• A. 350 J
• B. 490 J
• C. 150 J
• D. 250 J

Answer 1

The Correct Option is A

For an isobaric process:
The work done is calculated as:
\[w = P \Delta v = nR \Delta T = 100 \, \text{J}\]

The first law of thermodynamics is expressed as:
\[Q = \Delta U + W\]

For an ideal gas, the change in internal energy is:
\[\Delta U = \frac{f}{2} nR \Delta T\] Therefore,
\[\Delta Q = \frac{f}{2} nR \Delta T + nR \Delta T\]
\[\Delta Q = \left( \frac{f}{2} + 1 \right) nR \Delta T\]

Substituting \( f = 5 \) and \( nR \Delta T = 100 \, \text{J} \):
\[\Delta Q = \left( \frac{5}{2} + 1 \right) 100 = 350 \, \text{J}\]

Final Answer:
\[Q = 350 \, \text{J}\]