formulae

Celsius to Kelvin Conversion

The relationship to find absolute temperature is T(K) = T(C) + 273.15.

Mechanical Equivalent of Heat

1 calorie = 4.186 Joules.

Linear Expansion Formula

ΔL = αL₀ΔT, where α is the coefficient of linear expansion.

Volume Expansion Formula

ΔV = βV₀ΔT, where β is the coefficient of volume expansion.

Relationship between Coefficients of Expansion

β ≈ 3α for most solid materials.

Specific Heat Capacity Formula

Q = mcΔT, where m is mass, c is specific heat, and ΔT is the change in temperature.

Latent Heat Formula

Q = ±mL, where L is the latent heat of fusion or vaporization.

Conservation of Energy in Calorimetry

In an insulated system, ΣQ = 0.

Hydrostatic Pressure Formula

P = Patm + ρgh.

Ideal Gas Law (Molecular)

PV = NkBT, where N is the number of molecules and kB is Boltzmann's constant.

Ideal Gas Law (Molar)

PV = nRT, where n is the number of moles and R is the universal gas constant.

Boltzmann's Constant

kB = 1.38 x 10^-23 J/K.

Internal Energy (Ideal Gas)

Eint = (3/2)NkBT or Eint = (3/2)nRT.

Change in Internal Energy

ΔEint = (3/2)nRΔT.

First Law of Thermodynamics

ΔEint = Q - W, where Q is heat added and W is work done by the system.

Thermodynamic Work Formula

dW = PdV.

Total Work Done Formula

W = ∫ Vi Vf PdV.

Isochoric Process

dV = 0, therefore W = 0 and ΔEint = Q.

Isobaric Process

W = PΔV and Q = ΔEint + PΔV.

Isothermal Process

ΔEint = 0, therefore Q = W = nRT ln(Vf/Vi).

Adiabatic Process

Q = 0, so ΔEint = -W.

Heat at Constant Volume

Q = nCvΔT.

Heat at Constant Pressure

Q = nCpΔT.

Mayer's Relation

Cp = Cv + R.

Taylor Expansion Approximation

For small changes (x ≪ 1), (1+x)^n ≈ 1 + nx.