The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressure in the room remains 1 × 105 Pa. If Ni and Nf are the number of molecules in the room before and after heating, then Nf – Ni will be: (a) - 1.61 × 1023 (b) 1.38 × 1023 (c) 2.5 × 1025 (d) - 2.5 × 1025

Answer: (d). Room is open, so P and V stay fixed: N = PV/kT. Nf - Ni = PV/k(1/300 - 1/290) = 10⁵ × 301.38 × 10⁻²³ × (-(10)/(87000)). = 2.17 × 10²⁹ × (-1.15 × 10⁻⁴) ≈ -2.5 × 10²⁵. So the answer is (d) -2.5 × 10²⁵.

The temperature of an open room of volume 30 m3 increases from 17oC… | JEE Main 2017

Q71JEE Main 2017Medium

Gas Laws & Ideal Gas Equation

The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressure in the room remains 1 $\times$ 105 Pa. If Ni and Nf are the number of molecules in the room before and after heating, then Nf – Ni will be:

Show answer and solution

Answer: (d)

Room is open, so $P$ and $V$ stay fixed: $N = \frac{PV}{kT}$ .
$N_f - N_i = \frac{PV}{k}\left(\frac{1}{300} - \frac{1}{290}\right) = \frac{10^5 \times 30}{1.38 \times 10^{-23}} \times \left(-\frac{10}{87000}\right)$ .
$= 2.17 \times 10^{29} \times (-1.15 \times 10^{-4}) \approx -2.5 \times 10^{25}$ .
So the answer is (d) $-2.5 \times 10^{25}$ .

Report a mistake

Gas Laws & Ideal Gas Equation question from JEE Main 2017

More questions on Gas Laws & Ideal Gas Equation