Thermodynamics: Heat, Gases and the First Law
Thermodynamics distinguishes temperature from heat. Temperature is a measure of average particle kinetic energy and is measured in kelvin or degrees Celsius; T(K) = T(°C) + 273.15. Heat is energy transferred because of a temperature difference. Heating a substance may change its temperature, Q = mcΔT, or change its state at constant temperature, Q = mL, where c is specific heat capacity and L is specific latent heat.
Heat transfer occurs by conduction, convection and radiation. The ideal gas law is pV = nRT, with T always in kelvin. The first law of thermodynamics is usually written ΔU = Q − W, where Q is heat added to the system and W is work done by the system. In an isothermal process ΔU = 0; in an adiabatic process Q = 0; in an isobaric process work is pΔV; in an isochoric process W = 0.
Traps: using Celsius in the gas law; confusing specific heat capacity with latent heat; misapplying the sign convention in the first law; assuming that heat added always raises temperature, which fails during a phase change; and forgetting that isothermal means no change in internal energy for an ideal gas.
Worked example: heat 0.50 kg of water from 20 °C to 80 °C using c = 4180 J kg⁻¹ K⁻¹. Q = mcΔT = 0.50 × 4180 × 60 = 1.254 × 10⁵ J ≈ 125 kJ. If a 2 kW heater were used, the minimum time would be t = Q/P = 125 400 / 2000 ≈ 63 s, ignoring losses.