Heat and Thermodynamics 4 Question 16
18. The temperature of an open room of volume $30 \mathbf{m}^{3}$ increases from $17^{\circ} C$ to $27^{\circ} C$ due to the sunshine. The atmospheric pressure in the room remains $1 \times 10^{5} Pa$. If $n _i$ and $n _f$ are the number of molecules in the room before and after heating, then $n _f-n _i$ will be
(2017 Main)
(a) $1.38 \times 10^{23}$
(b) $2.5 \times 10^{25}$
(c) $-2.5 \times 10^{25}$
(d) $-1.61 \times 10^{23}$
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Solution:
- From $p V=n R T=\frac{N}{N _A} R T$
We have, $\quad n _f-n _i=\frac{p V N _A}{R T _f}-\frac{p V N _A}{R T _i}$
$\Rightarrow n _f-n _i=\frac{10^{5} \times 30}{8.3} \times 6.02 \times 10^{23} \cdot\left(\frac{1}{300}-\frac{1}{290}\right)$
$$ =-2.5 \times 10^{25} $$
$\therefore \quad \Delta n=-2.5 \times 10^{25}$
