Verified Solution • 2025–26 Session moderate

QPages 34-37: Q39: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q39 Solution: Show that the internal energy of the air treated as an ideal…

Show that the internal energy of the air treated as an ideal gas) contained in a room remains constant as the temperature changes between day and night. Assume that the atmospheric pressure around remains constant and the air in the room maintains this pressure by communicating with the surrounding through the windows, doors, etc. Use

R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}

Step-by-Step Verified Solution

**Answer:** The internal energy of the air in the room remains constant. **Step-by-Step Explanation:** For an ideal gas, internal energy

U = \frac{f}{2}nRT

where

f

is degrees of freedom. From ideal gas law:

nRT = PV

. So

U = \frac{f}{2}PV

. The room communicates with the surroundings through windows/doors, so the pressure inside equals atmospheric pressure

P_0

(constant). The volume

V

of the room is fixed. Therefore:

U = \frac{f}{2}P_0 V = \text{constant}

Even though temperature changes between day and night, the number of moles

n

changes (air enters/leaves), keeping

PV

and hence

U

constant.

All Questions in this Chapter

QPage 32: Q1 QPage 32: Q2 QPage 32: Q3 QPage 32: Q4 QPage 32: Q5 QPage 32: Q6 QPage 32: Q7 QPage 32: Q8 QPage 32: Q9 QPage 32: Q10 QPage 32: Q11 QPage 32: Q12 QPage 32: Q13 QPage 32: Q14 QPage 33: Q1 QPage 33: Q2 QPage 33: Q3 QPage 33: Q4 QPage 33: Q5 QPage 33: Q6 QPage 33: Q7 QPage 33: Q8 QPage 33: Q9 QPage 33: Q10 QPage 33: Q11 QPage 33: Q12 QPage 33: Q13 QPage 33: Q14 QPage 33: Q15 QPage 33: Q16 QPage 33: Q17 QPage 33: Q18 QPage 34: Q19 QPage 34: Q20 QPage 34: Q21 QPage 34: Q22 QPage 34: Q23 QPage 34: Q24 QPages 34-37: Q1 QPages 34-37: Q2 QPages 34-37: Q3 QPages 34-37: Q4 QPages 34-37: Q5 QPages 34-37: Q6 QPages 34-37: Q7 QPages 34-37: Q8 QPages 34-37: Q9 QPages 34-37: Q10 QPages 34-37: Q11 QPages 34-37: Q12 QPages 34-37: Q13 QPages 34-37: Q14 QPages 34-37: Q15 QPages 34-37: Q16 QPages 34-37: Q17 QPages 34-37: Q18 QPages 34-37: Q19 QPages 34-37: Q20 QPages 34-37: Q21 QPages 34-37: Q22 QPages 34-37: Q23 QPages 34-37: Q24 QPages 34-37: Q25 QPages 34-37: Q26 QPages 34-37: Q27 QPages 34-37: Q28 QPages 34-37: Q29 QPages 34-37: Q30 QPages 34-37: Q31 QPages 34-37: Q32 QPages 34-37: Q33 QPages 34-37: Q34 QPages 34-37: Q35 QPages 34-37: Q36 QPages 34-37: Q37 QPages 34-37: Q38 QPages 34-37: Q39 QPages 34-37: Q40 QPages 34-37: Q41 QPages 34-37: Q42 QPages 34-37: Q43 QPages 34-37: Q44 QPages 34-37: Q45 QPages 34-37: Q46 QPages 34-37: Q47 QPages 34-37: Q48 QPages 34-37: Q49 QPages 34-37: Q50 QPages 34-37: Q51 QPages 34-37: Q52 QPages 34-37: Q53 QPages 34-37: Q54 QPages 34-37: Q55 QPages 34-37: Q56 QPages 34-37: Q57 QPages 34-37: Q58 QPages 34-37: Q59 QPages 34-37: Q60 QPages 34-37: Q61 QPages 34-37: Q62

Related Learning Resources & Exam Preparation

Chapter Practice Bank

Practice all topic-wise questions from Kinetic Theory 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