Verified Solution • 2025–26 Session moderate

QPages 34-37: Q10: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q10 Solution: The temperature and pressure at Simla are 15.0�C and 72.0 cm of …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often plug the Celsius temperatures (15 °C, 35 °C) directly into $ ho=PM/RT$, forgetting that $T$ must be in Kelvin. Always add 273.15 to the Celsius value before using the ideal‑gas relation; otherwise the density ratio will be significantly off.

The temperature and pressure at Simla are 15.0�C and 72.0 cm of mercury and at Kalka these are 35.0�C and 76.0 cm of mercury. Find the ratio of air density at Kalka to the air density at Simla. Use R=8.314 J K−1 mol−1R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}

Step-by-Step Verified Solution

**Answer:** ρKalka/ρSimla=0.987\rho_{Kalka}/\rho_{Simla} = 0.987 **Step-by-Step Explanation:** Using ρ=PM/RT\rho = PM/RT:
ρKalkaρSimla=PKTSPSTK=76×28872×308=2188822176=0.987\frac{\rho_{Kalka}}{\rho_{Simla}} = \frac{P_K T_S}{P_S T_K} = \frac{76 \times 288}{72 \times 308} = \frac{21888}{22176} = 0.987

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