Thermodynamics

Chapter 10 measured how matter responds to heat. This chapter asks the harder question: what can you do with it? It opens by making the vocabulary precise — systems open, closed and isolated; state variables, extensive and intensive; and the zeroth law, which is what makes temperature a consistent property in the first place. Then the two ways energy crosses a boundary: heat and work, both path functions, against internal energy $U$, which is a state function — a distinction that decides more exam questions than any formula. The first law, $\Delta Q = \Delta U + \Delta W$, is conservation of energy with that distinction built in, and it forbids the perpetual motion machine of the first kind. For a gas it forces two specific heats rather than one, giving Mayer's relation $C_p - C_v = R$ and the ratio $\gamma = \frac{C_p}{C_v}$. The $P$-$V$ diagram then makes everything visual: the work done is the area under the curve, so it depends on the path, and a closed loop encloses the net work of a cycle. Four processes follow — isothermal ($\Delta U = 0$, $W = nRT\ln\frac{V_2}{V_1}$), adiabatic ($\Delta Q = 0$, $PV^\gamma$ constant, an adiabat always steeper than an isotherm), isobaric and isochoric (where no work is done at all). The second law then rules out what the first law allows: the Kelvin-Planck statement forbids a perfect engine, the Clausius statement forbids a perfect refrigerator, and between them they give time a direction. Heat engines convert heat to work with efficiency $\eta = 1 - \frac{Q_2}{Q_1}$; refrigerators and heat pumps run the same cycle backwards with a coefficient of performance that is routinely greater than one; and the Carnot engine sets the ceiling for all of them at $\eta = 1 - \frac{T_2}{T_1}$, a limit that depends on nothing but two temperatures. Carnot's theorem proves no engine can beat it, by an argument that couples a rival engine to a reversed Carnot engine and watches the pair break the second law. Topics the rationalised syllabus trimmed — the coefficient of performance, heat pumps, work as the area under a $P$-$V$ curve, and the values of $\gamma$ every adiabatic problem needs — are restored in full, because Boards, JEE Main and NEET ask about them every year. Dedicated JEE and NEET Corners follow, each with a full-length exam-pattern practice drill.