Question

If gas absorbs 150 J of heat and expands by \(450 \, \text{cm}^3\) against a constant pressure of \(2 \times 10^5 \, \text{N/m}^2\), then change in internal energy is

• A. \( -60 \, \text{J} \)
• B. \( 60 \, \text{J} \)
• C. \( 240 \, \text{J} \)
• D. \( -240 \, \text{J} \)

Hint:

Always convert cm\(^3\) to m\(^3\) before using \(W = P\Delta V\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
According to the First Law of Thermodynamics, the change in internal energy of a system is the difference between the heat added to the system and the work done by the system.
Step 2: Key Formula or Approach:
1. First Law: \( \Delta U = q - W \).
2. Work done (at constant pressure): \( W = P \Delta V \).
3. Conversion: \( 1 \text{ cm}^3 = 10^{-6} \text{ m}^3 \).
Step 3: Detailed Explanation:
Heat absorbed \( q = +150 \text{ J} \) (Positive because heat is absorbed by the system).
Expansion \( \Delta V = 450 \text{ cm}^3 = 450 \times 10^{-6} \text{ m}^3 \).
Constant pressure \( P = 2 \times 10^5 \text{ N/m}^2 \).
Work done by the gas:
\[ W = P \Delta V = (2 \times 10^5) \times (450 \times 10^{-6}) \]
\[ W = 2 \times 45 = 90 \text{ J} \]
Calculating change in internal energy:
\[ \Delta U = q - W = 150 - 90 = 60 \text{ J} \]
Step 4: Final Answer:
The change in internal energy is 60 J.