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Question:

The temperature of an open room of volume 30m³ increases from 17°C to 27°C due to the sunshine. The atmospheric pressure in the room remains 1×10⁵Pa. If nᵢ and nf are the number of molecules in the room before and after heating, then nf - nᵢ will be :

5.61×10²³

1.38×10²³

6.5×10²⁵

2.5×10²⁵

Solution:

PV=nRT ⇒ PV/R = nT
As P, V, R are remaining constant ⇒ nTᵢ = nfTf
Tᵢ = 290, Tf = 300
V = 30, P = 10⁵ Pa, R = 8.314
⇒ nᵢ = PVi/RTᵢ, nf = PfVf/RTf
for nf - nᵢ = PV/R (1/Tf - 1/Tᵢ) × Avogadro's number (A)
= 10⁵ × 30 / 8.314 (1/300 - 1/290) × 6.023 × 10²³
= 6.58 × 10²⁵