• # question_answer Two identical containers each of volume ${{V}_{0}}$ are joined by a pipe of negligible volume. The containers contain identical gases at temperature. To and pressure Po. One container is heated to temperature $2{{T}_{0}}$ while maintaining the other at the same temperature. The common pressure of the gas is P & n is the number of moles of gas in container at temperature$2{{T}_{0}}$. Mark the correct expression for this situation A) $P=2{{P}_{0}}$                               B) $P=\frac{3}{4}{{P}_{0}}$ C) $2{{P}_{0}}{{V}_{0}}=3nR{{T}_{0}}$       D) $3{{P}_{0}}{{V}_{0}}=2nR{{T}_{0}}$

Correct Answer: C

Solution :

${{P}_{0}}{{V}_{0}}={{n}_{0}}R{{T}_{0}}$[Initially for both containers] For container having temperature $2{{T}_{0}},P{{V}_{0}}=nR\times 2{{T}_{0}}$ For container having temperature ${{T}_{0}},P{{V}_{0}}=(2{{n}_{0}}-n)R{{T}_{0}}$ As number of moles of gas is conserved, so$2{{n}_{0}}=3n$$\Rightarrow$$2\frac{{{P}_{0}}{{V}_{0}}}{R{{T}_{0}}}=3\times \frac{P{{V}_{0}}}{2R{{T}_{0}}}=3n$$\Rightarrow$$P=\frac{4}{3}{{P}_{0}}$

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