Thermodynamics — Complete Formula

Basic Concepts

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Work Done	[W = \int P, dV]	[W] = work, [P] = pressure, [V] = volume	J	Area under P–V graph ⭐
Heat	[Q = mc\Delta T]	[Q] = heat, [m] = mass, [c] = specific heat, [\Delta T] = temperature change	J	Depends on material
Internal Energy	[\Delta U = Q – W]	[\Delta U] = change in internal energy	J	First law ⭐

💡 Memory Hint:
Energy balance → Heat supplied = increase in energy + work done

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
First Law	[Q = \Delta U + W]	[Q] = heat supplied, [W] = work done by system	J	Most important ⭐
Alternate Form	[\Delta U = Q – W]	—	J	Same equation rearranged

💡 Memory Hint:
Always track sign of Q and W ⚠️

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Equation	[PV = \text{constant}]	[P] = pressure, [V] = volume	—	Boyle’s law ⭐
Work Done	[W = nRT \ln\dfrac{V_2}{V_1}]	[n] = moles, [R] = gas constant, [T] = temperature	J	Important ⭐
Energy Change	[\Delta U = 0]	—	J	Depends only on temperature ⚠️

💡 Memory Hint:
Isothermal → temperature fixed → no change in internal energy

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Equation	[PV^\gamma = \text{constant}]	[\gamma] = heat capacity ratio	—	Important ⭐
Temperature Relation	[TV^{\gamma-1} = \text{constant}]	—	—	Alternate form
Work Done	[W = \dfrac{P_1V_1 – P_2V_2}{\gamma – 1}]	—	J	No heat exchange ⭐

💡 Memory Hint:
Adiabatic → no heat exchange

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Work Done	[W = 0]	—	J	No volume change ⭐
Heat Relation	[Q = \Delta U]	—	J	Entire heat changes internal energy

💡 Memory Hint:
Constant volume → no work done

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Work Done	[W = P(V_2 – V_1)]	—	J	Straight line in P–V graph ⭐
Heat Relation	[Q = nC_p \Delta T]	[C_p] = specific heat at constant pressure	J	Used frequently

💡 Memory Hint:
Constant pressure → simple work formula

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Specific Heat	[Q = mc\Delta T]	[c] = specific heat	J/kg·K	Basic relation
Molar Heat	[Q = nC\Delta T]	[C] = molar heat capacity	J/mol·K	Use in gas problems
Relation	[C_p – C_v = R]	[C_p], [C_v] = heat capacities	J/mol·K	Important ⭐
Gamma	[\gamma = \dfrac{C_p}{C_v}]	—	—	Used in adiabatic ⭐

💡 Memory Hint:
Always remember → [C_p – C_v = R]

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Pressure Relation	[P = \dfrac{1}{3}\rho v_{rms}^2]	[\rho] = density, [v_{rms}] = root mean square speed	Pa	Molecular view ⭐
RMS Speed	[v_{rms} = \sqrt{\dfrac{3RT}{M}}]	[M] = molar mass	m/s	Depends on temperature ⭐
Average KE	[K = \dfrac{3}{2}kT]	[k] = Boltzmann constant	J	Per molecule

💡 Memory Hint:
Temperature ∝ kinetic energy

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Efficiency	[\eta = 1 – \dfrac{T_2}{T_1}]	[T_1] = hot temp, [T_2] = cold temp	—	Maximum efficiency ⭐
Work Done	[W = Q_1 – Q_2]	[Q_1] = heat absorbed, [Q_2] = rejected	J	Energy balance

💡 Memory Hint:
Efficiency depends only on temperature

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