Volume versus temperature graphs for a given mass of an ideal gas are shown in figure. At two different values of constant pressure. What can be inferred about relation between `P_(1)` and `P_(2)` ?

Options

A. `P_(1) gt P_(2)`
B. `P_(1) = P_(2)`
C. `P_(1) lt P_(2)`
D. Data is insufficient

Explanation

We Know for an ideal gas
`pV = nRT rArr V= ((nR)/(p)) T`
`" Slope of the V - T graph " " " m=(dv)/(dT) =(nR)/(p) " "[m= "slopel of " V -t "graph"]`
` rArr " " m prop 1/p " "[:. nR = " constant"]`
`rArr " "p prop 1/m`
`" hence" " "(p_1))/(P_(2)) =(M_(2))/(M_(1)) lt 1 " " (##ARH_NCERT_EXE_PHY_XI_C12_S01_005_S01.png" width="80%">
Where `M_(1)` is slope of the graph correspoinding to `p_(1)` and similarly `m_(2)` is slope correspoinding to `p_(2)`
`rArr " " p_(2) lt p_(2) " or " p_(1) gt p_(2)`