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What is the first law of thermodynamics?

Class 11 PhysicsNCERT chapter: Thermodynamicsइसे हिंदी में पढ़ें

Exam-ready answer

The first law of thermodynamics states that the heat supplied to a system (ΔQ) is partly used to increase its internal energy (ΔU) and the rest in doing work on the environment (ΔW): ΔQ = ΔU + ΔW. It is the law of conservation of energy applied to any system in which energy transfer from or to the surroundings is taken into account.

Explanation

Consider a gas in a cylinder fitted with a movable piston. Its internal energy U is the sum of the kinetic and potential energies of its molecules. There are two ways to change U: supply heat ΔQ by placing the cylinder on a hot body, or let the gas do work ΔW by pushing the piston out. Energy cannot be created or destroyed, so the heat given must account for both effects.

Sign convention: ΔQ is positive when heat is supplied to the system, and ΔW is positive when work is done by the system. For a quasi-static process, the work done by the gas is ΔW = P ΔV, where P is the pressure and ΔV the change in volume. Internal energy is a state variable: it depends only on the state of the system, while ΔQ and ΔW depend on the path taken between two states.

Special cases: in an isothermal process of an ideal gas, temperature is constant, so ΔU = 0 and ΔQ = ΔW, meaning all the heat becomes work. In an adiabatic process, no heat is exchanged, so ΔQ = 0 and ΔW = −ΔU; a gas expanding adiabatically cools down. In an isochoric process, volume is constant, so ΔW = 0 and all the heat goes into internal energy.

Points to remember

  1. Statement: heat supplied = increase in internal energy + work done by the system.
  2. Equation: ΔQ = ΔU + ΔW, with ΔW = P ΔV for a quasi-static process.
  3. It is the law of conservation of energy applied to thermodynamic systems.
  4. Internal energy is a state variable; heat and work are not.
  5. Isothermal (ideal gas): ΔU = 0; adiabatic: ΔQ = 0; isochoric: ΔW = 0.

Exam tip

Write ΔQ = ΔU + ΔW with the meaning of each symbol and the sign convention. Then show one application, such as ΔU = 0 for an isothermal process of an ideal gas.

Questions students also ask

What is internal energy?
Internal energy of a system is the sum of the kinetic and potential energies of its molecules, measured in a frame where the centre of mass of the system is at rest. For an ideal gas it depends only on temperature.
Why does a gas cool when it expands adiabatically?
In an adiabatic process no heat enters, so ΔQ = 0. The expanding gas does work on the piston, and by the first law this work comes from its internal energy. So ΔU is negative and the temperature falls.
Can heat and work be called state variables?
No. The amounts of heat and work exchanged depend on the path by which the system goes from one state to another. Only their difference, ΔQ − ΔW, equals ΔU, which depends only on the initial and final states.

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