JEE Physics Thermodynamics Notes Set 02

Revision Notes for JEE Physics: Thermodynamics

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Review Thermodynamics for JEE Physics

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First Law and State Functions

1. \(\Delta U = Q - W\) where \(W\) is work done by the gas. \(U\) is a state function, while \(Q\) and \(W\) depend on the path.
2. Work \(W = \int P\,dV\) is the area under the P-V curve. It is positive for expansion.
3. For a complete cycle \(\Delta U = 0\), so net work equals net heat.

Processes of an Ideal Gas

ProcessConditionWorkHeat
Isothermal\(PV\) constant\(nRT\ln(V_2/V_1)\)\(Q = W\)
Isobaric\(P\) constant\(P\Delta V\)\(nC_p\Delta T\)
Isochoric\(V\) constant0\(nC_v\Delta T\)
Adiabatic\(PV^\gamma\), \(TV^{\gamma-1}\) constant\(\dfrac{P_1V_1 - P_2V_2}{\gamma - 1}\)0

1. \(C_p - C_v = R\), \(\gamma = C_p/C_v\). Monoatomic \(C_v = 3R/2\), diatomic \(5R/2\).
2. For a process \(V \propto T^m\) the molar heat capacity is \(C = C_v + R/m\), and \(W = mR\Delta T\) per mole.
3. For a mixture: \(C_v\) is the mole-weighted average of the \(C_v\) values, then \(\gamma = (C_v+R)/C_v\).
4. On V-T graph a line through the origin is an isobar, horizontal is isochoric and vertical is isothermal.

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