Physics - Heat & Thermo Question with Solution | TestHub

From ideal gas equation, $PV=nRT$

$\Rightarrow PV=\frac{N}{N_A}RT$, where $N=$ total number of molecules

$$\begin{gathered} \Rightarrow P=\frac{N}{V}\left(\frac{R}{N_A}\right)T \\ \Rightarrow P=\frac{N}{V}kT \end{gathered}$$

$\Rightarrow 1.38\times \left(1.01\times {10}^5\right)=\left(2\times {10}^{25}\right)\times \left(1.38\times {10}^{-23}\right)\times T$

$\Rightarrow 1.01\times {10}^5=2\times {10}^2\times T$

$T=\frac{1.01\times {10}^3}{2}\approx 500 \mathrm{K}$