Thermodynamics · Monoatomic Gas Cycle

Read the PV cycle through heat flow, temperature ratio and pressure ratio

The gas expands isothermally from a to b, cools at constant volume from b to c, and returns adiabatically from c to a. For a monoatomic gas, γ = 5/3, so the adiabatic leg fixes how Tc relates to Ta.

2026 Paper 1 Q7 · isothermal, isochoric, adiabatic
Statement check
Volume ratio V₂/V₁ 8.0
Cycle geometry
Process ab is isothermal, bc is isochoric, and ca is adiabatic for a monoatomic gas.
RelationT V²ᐟ³ = constant
VerdictA, B and C are correct
Isothermal abheat input
Isochoric bcheat released
Adiabatic cano heat exchange

Derivation path

01 / ADIABATIC LINK

Temperature at c comes from ca

For a monoatomic gas, γ = 5/3. Hence TVγ−1 = TV2/3 stays constant on ca.

Tc = Ta(V₁/V₂)2/3
02 / HEAT TERMS

Compare heat input and output

The isothermal branch absorbs heat, while the isochoric cooling branch releases heat.

Qab = nRT ln r, Qbc = 3nR(Ta − Tc)/2
03 / r = 8

Statements A and C become direct

At r = 8, Tc = Ta/4, so statement C is true. Also Qbc is smaller than Qab.

Qbc = 1.125 nRT, Qab ≈ 2.1 nRT
Correct statements
Statement A is true because Qbc < Qab for V₂/V₁ = 8.
Statement B is true because η depends only on the volume ratio r, not on the absolute isothermal temperature.
Statement C is true because Ta = 4Tc when r = 8.
Correct answer: A, B and C