Verified Solution • 2025–26 Session moderate

Q12.6: NCERT Physics - Part 2 KINETIC THEORY 12.6 Solution: Estimate the total number of air molecules (inclusive of…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently substitute the Celsius temperature (27) directly into the ideal gas equation, which is invalid because the relationship between pressure and temperature requires the absolute scale. Always convert to Kelvin ($T = 27 + 273 = 300$ K) before calculating $N$.

Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 m_ at a temperature of 27 �C and 1 atm pressure.

Step-by-Step Verified Solution

**Answer:** Number of molecules = 6.1×10266.1 \times 10^{26} **Step-by-Step Explanation:** Volume V=25.0V = 25.0 m_, T=27∘C=300T = 27^\circ\text{C} = 300 K, P=1P = 1 atm =1.013×105= 1.013 \times 10^5 Pa. Using PV=NkTPV = NkT:
N=PVkT=1.013×105×25.01.38×10−23×300=6.1×1026 moleculesN = \frac{PV}{kT} = \frac{1.013 \times 10^5 \times 25.0}{1.38 \times 10^{-23} \times 300} = 6.1 \times 10^{26} \text{ molecules}

All Questions in this Chapter

Q12.1 Q12.2 Q12.3 Q12.4 Q12.5 Q12.6 Q12.7 Q12.8 Q12.9 Q12.10

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