Verified Solution • 2025–26 Session moderate

QPages 34-37: Q23: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q23 Solution: Air is pumped into an automobile tyre's tube up to a pressure…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently use $P\propto T$ alone, forgetting the 2% increase in volume; this overestimates the final pressure. Always apply the full combined gas law $P_1V_1/T_1 = P_2V_2/T_2$ with temperatures in Kelvin and $V_2 = 1.02,V_1$.

Air is pumped into an automobile tyre's tube up to a pressure of 200 kPa in the morning when the air temperature is 20�C. During the day the temperature rises to 40�C and the tube expands by 2%. Calculate the pressure of the air in the tube at this temperature.

Step-by-Step Verified Solution

**Answer:**

P_2 = 209 \text{ kPa}

**Step-by-Step Explanation:**

P_1 = 200

kPa,

T_1 = 293

K,

T_2 = 313

K,

V_2 = 1.02 V_1

.

\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \Rightarrow P_2 = P_1 \times \frac{V_1}{V_2} \times \frac{T_2}{T_1} = 200 \times \frac{1}{1.02} \times \frac{313}{293} = 209 \text{ kPa}

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