Heat and Thermodynamics: laws, processes and engines
Heat and Thermodynamics: laws, processes and engines
NEB Class 12 Heat and Thermodynamics examines the first law, thermodynamic processes, kinetic theory, heat engines and transfer. Numerical questions often combine gas laws with energy accounting; short answers test why processes are isothermal, adiabatic or cyclic.
Core rules
- First law: Q = ΔU + W, where W is work done by the gas. For a small change, dQ = dU + dW.
- Ideal gas: ΔU = nCvΔT; Cp − Cv = R; for monatomic gas Cv = 3R/2.
- Isothermal: ΔT = 0, so ΔU = 0 and Q = W. Adiabatic: Q = 0, so ΔU = −W. Isochoric: W = 0, so Q = ΔU.
- Heat-engine efficiency η = W/Q₁ = 1 − Q₂/Q₁; Carnot limit η ≤ 1 − T₂/T₁ with absolute temperatures.
- Conduction rate through a slab: H = kA(ΔT)/L.
Worked example
Two moles of monatomic ideal gas expand adiabatically and do 400 J of work. Find ΔU and the temperature change. Adiabatic means Q = 0, so ΔU = −W = −400 J. For monatomic gas, ΔU = (3/2)nRΔT. Thus ΔT = 2ΔU/(3nR) = 2(−400)/(3 × 2 × 8.31) = −16.0 K. The gas cools by about 16 K; work comes from internal energy.
Traps
Mixing sign conventions for work done on vs by the gas; using Cp where Cv is required; assuming adiabatic means constant temperature; using Celsius in Carnot efficiency; forgetting that real engines cannot exceed the Carnot limit; ignoring heat loss in calorimetry.