question_answer

The pressure p for a gas is plotted against its absolute temperature T for two different volumes \[{{V}_{1}}\], and \[{{V}_{2}}\] where \[{{V}_{1}}>{{V}_{2}}\]. If p is plotted on y-axis and T on x-axis, then

A)                  the curve for \[{{V}_{1}}\]has greater slope than that for \[{{V}_{2}}\]

B)                  the curve for \[{{V}_{2}}\]has greater slope than that for \[{{V}_{1}}\]

C)                  both curves have same slope

D)                  the curves intersect at some point other than T = 0

Correct Answer: A

Solution :

                                                  As           \[{{\theta }_{1}}>{{\theta }_{2}}\Rightarrow \tan {{\theta }_{1}}>\tan {{\theta }_{2}}\]                 \[{{\left( \frac{T}{p} \right)}_{1}}>{{\left( \frac{T}{p} \right)}_{2}}\]                 Also from \[pV=\mu RT,\frac{T}{p}\propto V\Rightarrow {{V}_{1}}>{{V}_{2}}\]                 So, the curve for \[{{V}_{1}}\]has greater slope the than that for \[{{V}_{2}}.\]