A P-V diagram shows two curves starting from the same point A for the same ideal gas expanding to a larger volume. Curve 1 falls more steeply than curve 2. One curve is isothermal and the other adiabatic. Which statement is correct?
A
Curve 1 is adiabatic, because its slope is γ times that of the isothermal at A
B
Curve 1 is isothermal, because temperature stays constant
C
Curve 2 is adiabatic, because no heat enters the gas
D
Both curves have the same slope at A because they start at the same point
Show the answer
The answer is A.
For an isothermal, PV = constant and the slope is −P/V; for an adiabatic, PV^γ = constant and the slope is −γP/V. Since γ > 1, the adiabatic curve is steeper.
B.
The isothermal is the less steep curve, since its slope is only −P/V.
C.
No heat enters in an adiabatic process, but that makes it the steeper curve, not the gentler one.
D.
The slopes at A differ by the factor γ.
NCERT: Class 11 Physics, Chapter 11
Sample 2NEET level
Match List I (process on an ideal gas) with List II (condition that holds). List I: (A) Isothermal (B) Adiabatic (C) Isochoric (D) Isobaric List II: (I) Work done by the gas is zero (II) No heat is exchanged with the surroundings (III) Change in internal energy is zero (IV) Work done by the gas is P(V₂ − V₁) Choose the correct answer.
A
A-III, B-II, C-I, D-IV
B
A-II, B-III, C-I, D-IV
C
A-III, B-II, C-IV, D-I
D
A-I, B-II, C-III, D-IV
Show the answer
The answer is A.
For an ideal gas the internal energy depends only on temperature, so ΔU = 0 in an isothermal process; an adiabatic process has ΔQ = 0. At constant volume no work is done, and at constant pressure the work is P(V₂ − V₁).
B.
Swaps isothermal and adiabatic: in an adiabatic process the temperature changes, so ΔU is not zero.
C.
Swaps isochoric and isobaric: at constant volume ΔV = 0, so the work is zero.
D.
Swaps isothermal and isochoric: an isothermal expansion does work equal to the heat absorbed.
NCERT: Class 11 Physics, Chapter 11 (Thermodynamics), Thermodynamic processes
Practise Isothermal and adiabatic processes
Practice at the level you choose, with the answer after every question; timed tests with the answers when you submit. Every question is verified against NCERT first.