Question

The temperature of an open room of volume $30m^3$ increases form ${17}^{o}C$ to ${27}^{o}C$ 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 :

• A. $-2.5\times {10}^{25}$
• B. $-1.61\times {10}^{23}$
• C. $1.38\times {10}^{23}$
• D. $2.5\times {10}^{25}$

Answer 1

Answer: (A)

$-2.5\times {10}^{25}$

$PV=nRT$$\Rightarrow \frac{PV}{R}=nT$
As $P,V,R$ are remaining constant$\Rightarrow n_t{T}_i=n_1{T}_2$

$T_1=300,T_i=290$

$V=30,P={10}^{5}Pa,R=8.314$

$\Rightarrow n_i=\frac{P_i{V}_i}{R{T}_i},n_f=\frac{P_f{V}_f}{R{T}_f}$

or $n_f-n_i=\frac{PV}{R}(\frac{1}{T_f}-\frac{1}{T_i})\times A$

$=\frac{{10}^5\times 30}{8.314}(\frac{1}{300}-\frac{1}{290})$

$(n_f-n_i)\times 6.23\times {10}^{23}$
$=-2.58\times {10}^{25}$