Summary

This chapter developed WBCHSE Unit 8's account of thermodynamics in the order the syllabus lays it out. Thermal equilibrium is the condition of no net heat flow between two bodies in contact through a diathermic wall, and the Zeroth law (if $A$ and $B$ are each separately in thermal equilibrium with a third body $C$, then $A$ and $B$ are in thermal equilibrium with each other) is what makes temperature a well-defined, measurable quantity and justifies the use of thermometers. Internal energy $U$ is a state function, depending (for an ideal gas) only on temperature; heat $Q$ and work $W$ are path-dependent quantities, properties of a process rather than of a state. The first law of thermodynamics, $Q = \Delta U + W$, is energy conservation applied to a thermodynamic system, holding for every process without exception.

For an ideal gas, the two molar specific heats are related by $C_p - C_v = R$, derived from the first law applied at constant volume and at constant pressure; the ratio $\gamma = C_p/C_v$ is $5/3$ for a monatomic gas and $7/5$ for a diatomic gas. In an isothermal process ($T$ constant, $PV=\text{constant}$), $\Delta U = 0$ and $Q = W = nRT\ln(V_2/V_1)$. In an adiabatic process ($Q=0$, $PV^{\gamma}=\text{constant}$), $\Delta U = -W$ and $W = (P_1V_1-P_2V_2)/(\gamma-1) = nR(T_1-T_2)/(\gamma-1)$; the adiabatic curve is always steeper than the isothermal curve through the same point.

The second law of thermodynamics, in its Kelvin-Planck form (no engine can convert heat completely into work) and its Clausius form (heat cannot flow spontaneously from cold to hot), are logically equivalent statements that place a directional restriction on natural processes that the first law alone does not supply. A reversible process is an idealised, quasi-static, dissipation-free process that can be exactly undone; every real, finite-rate process is, to some degree, irreversible. …