Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
A gas in container A is in thermal equilibrium with another gas in container B both contains equal masses of the two gases in the respective containers. Which of the following can be true? (1) \[{{p}_{A}}{{V}_{A}}={{p}_{B}}{{V}_{B}}\] (2) \[{{p}_{A}}={{p}_{B}},{{V}_{A}}\ne {{V}_{B}}\] (3) \[\frac{{{p}_{A}}}{{{V}_{A}}}=\frac{{{p}_{B}}}{{{V}_{B}}}\] (4) \[{{p}_{A}}\ne {{p}_{B}},{{V}_{A}}={{V}_{B}}\]A) 1, 2 and 3 are correct.
B) 1 and 2 are correct.
C) 2 and 4 are correct.
D) 1 and 3 are correct.
Correct Answer: C
Solution :
According to problem mass of gases are equal so number of moles will not be equal ie, \[{{\mu }_{A}}\ne {{\mu }_{B}}\] From ideal gas equation \[pV=\mu RT\] \[\Rightarrow \] \[\frac{{{p}_{A}}{{V}_{A}}}{{{\mu }_{A}}}=\frac{{{p}_{B}}{{V}_{B}}}{{{\mu }_{B}}}\] [As temperature of the container are equal] From this relation it is clear that if \[{{p}_{A}}={{p}_{B}},\]then \[\frac{{{V}_{A}}}{{{V}_{B}}}=\frac{{{\mu }_{A}}}{{{\mu }_{B}}}\ne 1\] ie, \[{{V}_{A}}\ne {{V}_{B}}\] Similarly, if\[{{V}_{A}}={{V}_{B}}\]then\[\frac{{{P}_{A}}}{{{P}_{B}}}=\frac{{{\mu }_{A}}}{{{\mu }_{B}}}\ne 1\] ie, \[{{P}_{A}}\ne {{P}_{B}}\]
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