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11Class 11 Physics

Thermodynamics formulas

The first law and process formulas for Thermodynamics. Most marks come from getting the sign of work and heat right.

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All Physics formulas

First law

First law of thermodynamics
ΔQ=ΔU+ΔW\displaystyle \Delta Q = \Delta U + \Delta W

Here W is the work done by the gas.

Work by a gas
W=∫V1V2p dV\displaystyle W = \int_{V_1}^{V_2} p\,dV
Change in internal energy
ΔU=nCV ΔT\displaystyle \Delta U = nC_V\,\Delta T

For an ideal gas, in any process.

Mayer's relation
Cp−CV=R\displaystyle C_p - C_V = R
Ratio of specific heats
γ=CpCV\displaystyle \gamma = \frac{C_p}{C_V}

Processes (ideal gas)

Isothermal work
W=nRTln⁡V2V1\displaystyle W = nRT\ln\frac{V_2}{V_1}
Adiabatic relation
pVγ=constant\displaystyle pV^\gamma = \text{constant}
Adiabatic work
W=nR(T1−T2)γ−1\displaystyle W = \frac{nR(T_1 - T_2)}{\gamma - 1}
Isobaric work
W=p ΔV\displaystyle W = p\,\Delta V
Isochoric work
W=0\displaystyle W = 0

Engines

Efficiency of a heat engine
η=WQ1=1−Q2Q1\displaystyle \eta = \frac{W}{Q_1} = 1 - \frac{Q_2}{Q_1}
Carnot efficiency
η=1−T2T1\displaystyle \eta = 1 - \frac{T_2}{T_1}

Temperatures in kelvin.

Coefficient of performance
β=Q2W\displaystyle \beta = \frac{Q_2}{W}

For a refrigerator.

Where students slip up

  • Mixing the physics and chemistry sign conventions. Physics usually writes ΔQ = ΔU + W, with W done by the gas, while chemistry uses ΔU = q + w, with w done on the gas.
  • Using ΔU = nCᵥΔT only for constant-volume processes. For an ideal gas it holds for every process.
  • Using Celsius in Carnot efficiency.

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