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  • Two containers of equal volume contain the same gas at pressure and <img alt="\mathrm{p_{2

Two containers of equal volume contain the same gas at pressure \mathrm{p_{1}}and \mathrm{p_{2}} and absolute temperatures \mathrm{T_{1}} and \mathrm{T_{2}} respectively. On joining the vessels, the gas reaches a common pressure \mathrm{p} and a common temperature \mathrm{T}.The ratio \mathrm{p / T}is equal to

Option: 1

\frac{\mathrm{p}_{1}}{\mathrm{~T}_{1}}+\frac{\mathrm{p}_{2}}{\mathrm{~T}_{2}}


Option: 2

\frac{1}{2}\left[\frac{\mathrm{p}_{1}}{\mathrm{~T}_{1}}+\frac{\mathrm{p}_{2}}{\mathrm{~T}_{2}}\right]


Option: 3

\frac{\mathrm{p}_{1} \mathrm{~T}_{2}+\mathrm{p}_{2} \mathrm{~T}_{1}}{\mathrm{~T}_{1}+\mathrm{T}_{2}}


Option: 4

\frac{\mathrm{p}_{1} \mathrm{~T}_{2}-\mathrm{p}_{2} \mathrm{~T}_{1}}{\mathrm{~T}_{1}-\mathrm{T}_{2}}


Answers (1)

best_answer

For a closed system, the total mass of gas or the number of moles remains constant.

\mathrm{P}_{1} \mathrm{~V}=\mathrm{n}_{1} \mathrm{RT}_{1}, \mathrm{p}_{2} \mathrm{~V}=\mathrm{n}_{2} \mathrm{RT}_{2}, \mathrm{p}(2 \mathrm{~V})=\left(\mathrm{n}_{1}+\mathrm{n}_{2}\right) \mathrm{RT}

\mathrm{P}(2 \mathrm{~V})=\left(\frac{\mathrm{P}_{1} \mathrm{~V}}{\mathrm{RT}_{1}}+\frac{\mathrm{P}_{2} \mathrm{~V}}{\mathrm{RT}_{2}}\right) \mathrm{RT} \Rightarrow \frac{\mathrm{P}}{\mathrm{T}}=\frac{1}{2}\left[\frac{\mathrm{P}_{1}}{\mathrm{~T}_{1}}+\frac{\mathrm{P}_{2}}{\mathrm{~T}_{2}}\right]

Posted by

Deependra Verma

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