Kinetic theory and the first law

MDCAT Physics · Physics · Thermodynamics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A gas presses on its container because its molecules hit the walls and bounce back. In the kinetic theory, the absolute temperature of an ideal gas is proportional to the average translational kinetic energy of its molecules. The internal energy of an ideal gas depends on its temperature only.

The first law of thermodynamics is the conservation of energy for heat and work: the heat supplied to a gas goes into raising its internal energy and into work done by the gas.

Four special processes are tested: isothermal (constant temperature), adiabatic (no heat enters or leaves), isobaric (constant pressure) and isochoric (constant volume). For each one, decide which term of the first law is zero.

Rules to remember

Common mistake

Using Celsius temperatures in gas and kinetic energy ratios. Change to kelvin first: doubling the kinetic energy of a gas at 27 °C means going from 300 K to 600 K, which is 327 °C, not 54 °C.

Worked example

A gas is given 500 J of heat and expands at a constant pressure of 1.0 × 105 Pa from 2.0 × 10−3 m3 to 4.0 × 10−3 m3. What is the change in its internal energy?

  1. Work done by the gas W = PΔV = 1.0 × 105 × (4.0 − 2.0) × 10−3 = 200 J.
  2. First law: ΔU = Q − W.
  3. ΔU = 500 − 200 = 300 J.

Answer: The internal energy rises by 300 J

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