Thermodynamics
The Thermodynamics domain tests heat versus temperature, thermal energy transfer, the ideal gas law, the first and second laws, PV diagrams, and heat-engine efficiency. Most missed marks come from unit errors-Celsius in gas-law calculations-or from ignoring a phase change.
Heat and temperature
Temperature measures average molecular kinetic energy; heat is energy transferred because of a temperature difference. For a temperature change with no phase change, Q = mcΔT. During a phase change, temperature stays constant and Q = mL, where L is the latent heat of fusion or vaporization.
Gas laws
For an ideal gas, PV = nRT, with T in kelvin. At constant volume, P/T is constant; at constant temperature, PV is constant. Always convert °C to K by adding 273.
First law
ΔU = Q − W, where W is work done by the gas. Work equals the area under the curve on a PV diagram; at constant pressure W = PΔV. Isothermal: ΔU = 0. Adiabatic: Q = 0. Constant volume: W = 0, so ΔU = Q.
Second law and engines
Heat flows spontaneously from hot to cold, and the entropy of an isolated system increases. Engine efficiency is e = W/Q_H = 1 − Q_C/Q_H. The Carnot limit is e_max = 1 − T_C/T_H, with both temperatures in kelvin; no real engine between the same reservoirs exceeds it.
Worked example
How much heat is needed to warm 0.50 kg of water from 20 °C to 80 °C? (c = 4186 J/kg·°C) ΔT = 60 °C, so Q = mcΔT = 0.50 × 4186 × 60 ≈ 1.26 × 10⁵ J. A 60 °C rise equals a 60 K rise, so a temperature difference may stay in Celsius; only absolute temperatures must be converted.
Traps
- Putting Celsius temperatures into PV = nRT or the Carnot formula.
- Using mcΔT across a phase change instead of mL.
- Reversing the sign of work in ΔU = Q − W.
- Reporting efficiency above 1 or below 0.
- Forgetting that Q_C is the heat rejected, not the heat absorbed.