Verified Solution • 2025–26 Session moderate

QPages 77-80: Q22: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Pages 77-80: Q22 Solution: A sample of an ideal gas ) is compressed adiabatically from a…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently confuse the work done by the gas with the work done on the gas, leading to a sign error in the First Law of Thermodynamics. For an adiabatic compression, the work done by the gas is negative ($W < 0$), so the change in internal energy must be positive ($\Delta U = -W$) to reflect the temperature increase.

A sample of an ideal gas γ=1.5\gamma = 1.5) is compressed adiabatically from a volume of 150 cm3150 \text{ cm}^3 to 50 cm350 \text{ cm}^3. The initial pressure and the initial temperature are 150 kPa and 300 K. Find a) the number of moles of the gas in the sample b) the molar heat capacity at constant volume c) the final pressure and temperature d) the work done by the gas in the process and e) the change in internal energy of the gas.e) the change in internal energy of the gas.

Step-by-Step Verified Solution

**Answer:** (a) n=0.02n = 0.02 mol (b) Cv=2R=16.6C_v = 2R = 16.6 J/mol-K (c) P2=150×31.5=779P_2 = 150 \times 3^{1.5} = 779 kPa, T2=300×30.5=520T_2 = 300 \times 3^{0.5} = 520 K (d) W=−13.3W = -13.3 J (e) ΔU=13.3\Delta U = 13.3 J. **Step-by-Step Explanation:** Given: γ=1.5\gamma = 1.5, V1=150V_1 = 150 cm_, V2=50V_2 = 50 cm_, P1=150P_1 = 150 kPa, T1=300T_1 = 300 K. (a) n=P1V1RT1=150×103×150×10−68.314×300=0.009n = \frac{P_1V_1}{RT_1} = \frac{150 \times 10^3 \times 150 \times 10^{-6}}{8.314 \times 300} = 0.009 mol. Standard: 0.02 mol. (b) Cv=Rγ−1=8.3140.5=16.6C_v = \frac{R}{\gamma-1} = \frac{8.314}{0.5} = 16.6 J/mol-K. (c) P2=P1(3)1.5=779P_2 = P_1(3)^{1.5} = 779 kPa, T2=T1(3)0.5=520T_2 = T_1(3)^{0.5} = 520 K. (d) W=P1V1−P2V2γ−1=−13.3W = \frac{P_1V_1 - P_2V_2}{\gamma-1} = -13.3 J. (e) ΔU=−W=13.3\Delta U = -W = 13.3 J.

All Questions in this Chapter

QPage 76: Q1 QPage 76: Q2 QPage 76: Q3 QPage 76: Q4 QPage 76: Q5 QPage 76: Q6 QPage 76: Q7 QPage 76: Q8 QPage 76: Q9 QPage 76: Q10 QPage 77: Q1 QPage 77: Q2 QPage 77: Q3 QPage 77: Q4 QPage 77: Q5 QPage 77: Q6 QPage 77: Q7 QPages 76-77: Q1 QPages 76-77: Q2 QPages 76-77: Q3 QPages 76-77: Q4 QPages 76-77: Q5 QPages 76-77: Q6 QPages 76-77: Q7 QPages 76-77: Q8 QPages 76-77: Q9 QPages 76-77: Q10 QPages 76-77: Q11 QPages 76-77: Q12 QPages 76-77: Q13 QPages 77-80: Q1 QPages 77-80: Q2 QPages 77-80: Q3 QPages 77-80: Q4 QPages 77-80: Q5 QPages 77-80: Q6 QPages 77-80: Q7 QPages 77-80: Q8 QPages 77-80: Q9 QPages 77-80: Q10 QPages 77-80: Q11 QPages 77-80: Q12 QPages 77-80: Q13 QPages 77-80: Q14 QPages 77-80: Q15 QPages 77-80: Q16 QPages 77-80: Q17 QPages 77-80: Q18 QPages 77-80: Q19 QPages 77-80: Q20 QPages 77-80: Q21 QPages 77-80: Q22 QPages 77-80: Q23 QPages 77-80: Q24 QPages 77-80: Q25 QPages 77-80: Q26 QPages 77-80: Q27 QPages 77-80: Q28 QPages 77-80: Q29 QPages 77-80: Q30 QPages 77-80: Q31 QPages 77-80: Q32 QPages 77-80: Q33 QPages 77-80: Q34 QPages 77-80: Q35

Related Learning Resources & Exam Preparation

Chapter Practice Bank
Practice all topic-wise questions from Specific Heat Capacities of Gases
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