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

Answer

A

Explanation

We know for an ideal gas,
`" "pV=nRTrArrV=((nR)/(p))T`
Slope of V-T graph, m `=(dV)/(dT)=(nR)/p` [m = slope of V-t graph]
`rArr" "m prop1/p" "[nR="constant"]`
`rArr" " pprop1/m`
Hence, `" "(p_(1))/(p_(2))=(m_(2))/(m_(1))lt 1 [{:("p=pressure, V = volume"),("n=number of moles of gases"),("R=gas constant"),("T=temperature")]:}`
where, `m_(1)` is slope of the graph corresponding to `p_(1)` and similarly `m_(2)` is slope corresponding to `p_(2^.)`
`rArr" "p_(2) lt p_(1)or p_(1)gt p_(2)`