Question:
An ideal gas goes through a reversible cycle \(a\to b\to c\to d\) has the V - T diagram shown below. Process \(d\to a\) and \(b\to c\) are adiabatic.
The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) :
An ideal gas goes through a reversible cycle \(a\to b\to c\to d\) has the V - T diagram shown below. Process \(d\to a\) and \(b\to c\) are adiabatic.
The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) :
The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) :
Show Hint
a-b and c-d are straight lines in the V-T plot (isobaric); b-c and d-a are adiabatic with P proportional to V^-gamma, i.e. curves steep at the top-left end and flatter at the lower-right end.
Updated On: Nov 11, 2026
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The Correct Option is C
Solution and Explanation
V-T diagram: a to b is a straight line (V proportional to T), so an isobaric expansion at the higher pressure; c to d is a straight line (isobaric compression) at the lower pressure (its V/T slope is larger, and V/T = nR/P). b to c is an adiabatic expansion (V rises, T falls, so P falls) and d to a is an adiabatic compression (V falls, T rises, so P rises).
In the P-V plane: a to b is a horizontal top line going right; b to c a falling adiabat; c to d a horizontal bottom line going left; d to a a rising adiabat. a and b are on top, d and c at the bottom, with d to the right of a and c to the right of b (V_d > V_a and V_c > V_b).
Adiabats obey \(P\propto V^{-\gamma}\): they are convex towards the origin (steep at high P and small V, flatter at low P and large V). Options (2) and (4) draw the adiabats the other way round (shallow at the top, steep at the bottom), which is impossible, leaving (1) and (3), which show convex adiabats with correct corner positions.
Answer: (3) (the loop with convex adiabats)
In the P-V plane: a to b is a horizontal top line going right; b to c a falling adiabat; c to d a horizontal bottom line going left; d to a a rising adiabat. a and b are on top, d and c at the bottom, with d to the right of a and c to the right of b (V_d > V_a and V_c > V_b).
Adiabats obey \(P\propto V^{-\gamma}\): they are convex towards the origin (steep at high P and small V, flatter at low P and large V). Options (2) and (4) draw the adiabats the other way round (shallow at the top, steep at the bottom), which is impossible, leaving (1) and (3), which show convex adiabats with correct corner positions.
Answer: (3) (the loop with convex adiabats)
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