AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
PV = nRT γ adiabatic change : pV = constant isothermal change : pV =…
Full specification wording
Non-flow processes (A-level only): pV = nRT γ adiabatic change : pV = constant isothermal change : pV = constant at constant pressure W = pΔV Application of first law of thermodynamics to the above processes.
The ideal gas equation pV = nRT links pressure, volume, amount and temperature.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 2 of 2
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The ideal gas equation pV = nRT links pressure, volume, amount and temperature. For an isothermal change, T is fixed so pV is constant, giving a smooth p–V curve. For an adiabatic change, no heat flows, so pV^γ is constant, where γ = C_p/C_V; the curve is steeper than an isotherm. At constant pressure, work done by the gas is W = pΔV. The first law ΔU = Q − W then explains each path: isothermal has ΔU = 0 so Q = W; adiabatic has Q = 0 so ΔU = −W; constant pressure has both heat and work; constant volume has W = 0 so Q = ΔU.
What earns the marks
- Uses pV = nRT to relate state variables and to show that pV is constant when T is constant.
- States and applies pV^γ = constant for an adiabatic change, identifying γ as the ratio of principal molar heat capacities.
- Calculates work done at constant pressure using W = pΔV, with consistent units.
- Applies ΔU = Q − W to each process, setting the appropriate term to zero.
- Compares isothermal and adiabatic curves on a p–V diagram, noting the adiabatic curve is steeper through the same point.
- Uses the first law to deduce temperature change from work done when Q = 0.
Common mistakes and how to put them right
Writing pV = constant for an adiabatic change.
Put it right: Use pV^γ = constant, where γ is greater than 1.
Treating W = pΔV as valid for all processes.
Put it right: It applies only at constant pressure, otherwise use the area under the p–V curve.
Forgetting that γ is dimensionless and greater than 1 for gases.
Put it right: γ = C_p/C_V and is about 1.4 for diatomic gases.
Exam tips
- Quote the equation you use and state the condition that makes it valid.
- Check units of p and V before substituting into W = pΔV.
- For adiabatic questions, start from Q = 0 and link work done to internal energy change.
Try the lesson
The start of the Non-flow processes (A-level only): pV = nRT γ adiabatic change : pV = constant isothermal change : pV = constant at constant pressure W = pΔV Application of first law of thermodynamics to the above processes. lesson, made from checked teaching notes for this specification point.
Have a go first
For an ideal gas, which equation of state links pressure p, volume V, amount in moles n and thermodynamic temperature T?
Listen
The ideal gas equation pV = nRT links pressure, volume, amount and temperature. For an isothermal change, T is fixed so pV is constant, giving a smooth p–V curve. For an adiabatic change, no heat flows, so pV^γ is constant, where γ = C_p/C_V; the curve is steeper than an isotherm. At constant pressure, work done by the gas is W = pΔV. The first law ΔU = Q − W then explains each path: isothermal has ΔU = 0 so Q = W; adiabatic has Q = 0 so ΔU = −W; constant pressure has both heat and work; constant volume has W = 0 so Q = ΔU. A strong answer earns marks for these points. Uses pV = nRT to relate state variables and to show that pV is constant when T is constant. States and applies pV^γ = constant for an adiabatic change, identifying γ as the ratio of principal molar heat capacities. Calculates work done at constant pressure using W = pΔV, with consistent units. Applies ΔU = Q − W to each process, setting the appropriate term to zero. A common slip: Writing pV = constant for an adiabatic change. Instead, use pV^γ = constant, where γ is greater than 1. Exam tip: Quote the equation you use and state the condition that makes it valid.
See it
Key words
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Ideal gas equation
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Adiabatic change
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Isothermal change
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Work done by a gas
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See every definition
- Ideal gas equation
- pV = nRT links pressure, volume, amount and temperature.
- Adiabatic change
- No heat flows, so pV^γ is constant, where γ = C_p/C_V; the curve is steeper than an isotherm.
- Isothermal change
- T is fixed so pV is constant, giving a smooth p–V curve.
- Work done by a gas
- At constant pressure, work done by the gas is W = pΔV.
Label the diagram
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