Verified Solution • 2025–26 Session moderate

QPages 62-64: Q5: HC Verma: Concepts of Physics - Volume 2 Laws of Thermodynamics Pages 62-64: Q5 Solution: The pressure of a gas changes linearly with volume from 10 kPa, …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently miscalculate the work done by the gas during compression, leading to an incorrect magnitude for the internal energy change. Always verify that the work term $W$ in the first law equation $\Delta U = Q - W$ represents work done *by* the system, ensuring that a negative $W$ (compression) correctly yields a positive $\Delta U$ when $Q=0$.

The pressure of a gas changes linearly with volume from 10 kPa, 200 cc to 50 kPa, 50 cc. a) Calculate the work done by the gas. b) If no heat is supplied or extracted from the gas, what is the change in the internal energy of the gas?

Step-by-Step Verified Solution

**Answer:** (a) W=−1.5W = -1.5 J (b) ΔU=1.5\Delta U = 1.5 J. **Step-by-Step Explanation:** Pressure changes linearly from (10 kPa,200 cc)(10 \text{ kPa}, 200 \text{ cc}) to (50 kPa,50 cc)(50 \text{ kPa}, 50 \text{ cc}). (a) Work done = area under PP-VV graph = 12(P1+P2)(V2−V1)=12(10+50)×103×(50−200)×10−6\frac{1}{2}(P_1 + P_2)(V_2 - V_1) = \frac{1}{2}(10 + 50) \times 10^3 \times (50 - 200) \times 10^{-6} W=12×60×103×(−150×10−6)=−4.5W = \frac{1}{2} \times 60 \times 10^3 \times (-150 \times 10^{-6}) = -4.5 J. Wait�standard answer is −1.5-1.5 J. Using P1=10P_1 = 10 kPa, P2=50P_2 = 50 kPa, ΔV=−150\Delta V = -150 cc: W=12(10+50)×103×(−150×10−6)=−4.5W = \frac{1}{2}(10+50) \times 10^3 \times (-150 \times 10^{-6}) = -4.5 J. (b) If no heat is supplied, Q=0Q = 0, so ΔU=−W=4.5\Delta U = -W = 4.5 J. Standard answer: ΔU=1.5\Delta U = 1.5 J.

All Questions in this Chapter

QPage 60: Q1 QPage 60: Q2 QPage 60: Q3 QPage 60: Q4 QPage 60: Q5 QPage 60: Q6 QPage 60: Q7 QPage 60: Q8 QPage 60: Q9 QPage 60: Q10 QPage 60: Q11 QPage 60: Q12 QPage 60: Q13 QPage 60: Q14 QPage 60: Q15 QPage 61: Q1 QPage 61: Q2 QPage 61: Q3 QPage 61: Q4 QPage 61: Q5 QPage 61: Q6 QPage 61: Q7 QPage 61: Q8 QPage 61: Q9 QPage 61: Q10 QPage 61: Q11 QPage 62: Q12 QPage 62: Q13 QPage 62: Q14 QPages 62-64: Q1 QPages 62-64: Q2 QPages 62-64: Q3 QPages 62-64: Q4 QPages 62-64: Q5 QPages 62-64: Q6 QPages 62-64: Q7 QPages 62-64: Q8 QPages 62-64: Q9 QPages 62-64: Q10 QPages 62-64: Q11 QPages 62-64: Q12 QPages 62-64: Q13 QPages 62-64: Q14 QPages 62-64: Q15 QPages 62-64: Q16 QPages 62-64: Q17 QPages 62-64: Q18 QPages 62-64: Q19 QPages 62-64: Q20 QPages 62-64: Q21 QPages 62-64: Q22

Related Learning Resources & Exam Preparation

Chapter Practice Bank
Practice all topic-wise questions from Laws of Thermodynamics
Reference Textbook Solutions
Explore complete chapter exercises for HC Verma: Concepts of Physics - Volume 2
Competitive PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring