Question 194: Thermodynamics & KTG

Question

The temperature of a gas having $$2.0 	imes 10^{25}$$ molecules per cubic meter at $$1.38 \mathrm{~atm}$$ (Given, $$\mathrm{k}=1.38 	imes 10^{-23} \mathrm{JK}^{-1}$$) is :

Accepted Answer

$$\begin{aligned}
& \mathrm{PV}=\mathrm{nRT} \
& \mathrm{PV}=\frac{\mathrm{N}}{\mathrm{N}_{\mathrm{A}}} \mathrm{RT} \
& \mathrm{N}=	ext { Total no. of molecules } \
& \mathrm{P}=\frac{\mathrm{N}}{\mathrm{V}} \mathrm{kT} \
& 1.38 	imes 1.01 	imes 10^5=2 	imes 10^{25} 	imes 1.38 	imes 10^{-23} 	imes \mathrm{T} \
& 1.01 	imes 10^5=2 	imes 10^2 	imes \mathrm{T} \
& \mathrm{T}=\frac{1.01 	imes 10^3}{2} \approx 500 \mathrm{~K}
\end{aligned}$$

Answer

500 K

Answer

300 K

Answer

200 K

Answer

100 K

Thermodynamics & KTG

The temperature of a gas having $2.0 \times 10^{25} molecules per cubic meter at 1.38 \mathrm{~atm} (Given, \mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}$) is :

Choose the correct answer: