The volume versus temperature graphs for a given mass of an ideal gas are shown in the figure at two different values of constant pressure. What can be inferred about relation between \(\mathrm{P_1}\) and \(\mathrm{P_2}\)?

                  
1. \(\mathrm{P_1}>\mathrm{P_2}\)
2. \(\mathrm{P_1}=\mathrm{P_2}\)
3. \(\mathrm{P_1}<\mathrm{P_2}\)
4. data is insufficient

(1) Hint: The slope of the V-T graph gives the pressure.
Step 1: Find the slope of the two graphs.
We know for an ideal gas,
                        pV=nRTV=nRPT
Slope of the V— T graph, m=dVdT=nRP         [m = slope of V-T graph]
             m1P                                                        [ nR = constant]
             P1m
Step 2: Find the relation between two pressures.
hence,     P1P2=m2m1<1                 [P=pressure]
where m1 is the slope of the graph corresponding to P1 and similarly m2 is the slope corresponding to P2.
                  P2<P1 or P1>P2