Thermal Physics: Temperature, Ideal Gases, Internal Energy and Thermodynamics
Temperature and ideal gases
Thermodynamic temperature uses kelvin: T/K = θ/°C + 273.15. The ideal gas equation is pV = nRT, with p in Pa, V in m³ and T in K. For a fixed mass, pV/T is constant. The kinetic theory gives pV = ⅓Nm<c²>, so the mean kinetic energy of a molecule is (3/2)kT for a monatomic gas.
Internal energy and thermodynamics
Internal energy is the sum of random kinetic and potential energies of molecules. For an ideal gas, potential energy is zero, so U depends only on T. First law: ΔU = Q − W, where W is work done by the gas. W = pΔV at constant pressure. Isothermal means ΔT = 0; adiabatic means Q = 0.
Specific and latent heat
Q = mcΔT for a temperature change; Q = mL for a phase change at constant temperature. Specific heat capacity is per kilogram; molar heat capacity is per mole.
Worked example
2.0 mol of monatomic ideal gas occupies 0.050 m³ at 300 K. p = nRT/V = 2.0 × 8.31 × 300/0.050 = 1.0 × 10^5 Pa. Heated at constant volume to 600 K: ΔU = (3/2)nRΔT = 1.5 × 2.0 × 8.31 × 300 = 7.5 kJ. Since volume is constant, W = 0, so Q = 7.5 kJ.
Traps
Using Celsius in pV = nRT; mixing molar and specific heat capacities; getting the sign of work wrong; assuming temperature rises during melting; using the monatomic factor for a diatomic gas.