Thermodynamics
Thermodynamics
The exam tests the laws of thermodynamics, identifying processes on p–V diagrams, and simple energy and efficiency balances.
Concepts
- System, boundary, surroundings. Closed system: fixed mass; open system: mass crosses the boundary; isolated system: no heat and no work.
- Zeroth law underlies temperature measurement; first law: Q = ΔU + W (energy conservation); second law: heat flows spontaneously from hot to cold and no engine reaches 100 % efficiency.
- Intensive properties (pressure, temperature) do not depend on mass; extensive properties (volume, mass, total energy) do.
- Processes: isothermal (T constant, pV = C), adiabatic (Q = 0, pV^γ = C), isobaric (p constant), isochoric (V constant, so W = 0).
- For an ideal gas cp − cv = R and γ = cp/cv.
- Carnot efficiency η = 1 − T₂/T₁, with both temperatures in kelvin.
Worked example
A Carnot engine works between 500 K and 300 K and receives 1000 kJ. η = 1 − 300/500 = 0.40, i.e. 40 %. Work output = 0.40 × 1000 = 400 kJ; heat rejected = 1000 − 400 = 600 kJ. Note that the rejected heat is not η × T₂; use the energy balance.
Traps
- Putting Celsius values into 1 − T₂/T₁; convert first (227 °C = 500 K).
- Mixing gauge and absolute pressure: p_abs = p_gauge + p_atm.
- Expecting work from an isochoric process, where W = 0.
- Saying entropy falls in an irreversible adiabatic process - it rises.
- Treating heat and work as properties; both are path functions.