Question

For the given P-V graph of an ideal gas, chose the correct V-T graph. Process $1 \rightarrow 2$ is adiabatic. (Graphs are schematic and not to scale).


(A)

(B)

(C)

(D)

Answer 1

Hint: In order to solve this question, we will observe the each path of the given PV diagram cycle, and then using concepts of constant pressure, constant temperature, and constant volume and with an understanding of linear and non-linear graphs we will match the correct graph for the representation of VT diagram of same corresponding PV diagram.

Complete answer:
From the given PV diagram let us observe the path $2 \rightarrow 3$ which is kept at constant pressure as we know at constant pressure-volume is directly proportional to the temperature which means the graph for path $2 \rightarrow 3$ will be a straight line passing through the origin, so only graph in given options (B) and (D) have this condition.

Now, on observing the path $1 \rightarrow 3$ from the PV diagram we see that it’s kept at the constant volume it means in the VT diagram path $1 \rightarrow 3$ must be kept at a constant volume so from options only (B) and (D have this condition.

Now, the last path $1 \rightarrow 2$ in the PV diagram is adiabatic so in the VT diagram it can’t be a straight line it must a curve, only option (A) fulfills this condition.

Hence, option (A) is the correct answer.

Note: It should be remembered that when the volume is directly proportional to temperature the equation becomes $V = kT$ which is an equation of a straight line passing through origin and adiabatic processes have curved graph because of the equation $P{V^{\gamma} } = K$.