10Class 11 Physics

Thermal Properties of Matter formulas

Thermal expansion, calorimetry and heat transfer formulas. Watch your units, since many of these need kelvin and not degrees Celsius.

Temperature and expansion

Temperature scales
TC100=TF−32180,TK=TC+273.15\displaystyle \frac{T_C}{100} = \frac{T_F - 32}{180}, \quad T_K = T_C + 273.15
Linear expansion
ΔL=αL ΔT\displaystyle \Delta L = \alpha L\,\Delta T
Area and volume expansion
ΔA=βA ΔT,ΔV=γV ΔT\displaystyle \Delta A = \beta A\,\Delta T, \quad \Delta V = \gamma V\,\Delta T
Relation between coefficients
β=2α,γ=3α\displaystyle \beta = 2\alpha, \quad \gamma = 3\alpha

For isotropic solids.

Calorimetry

Heat and specific heat
Q=mc ΔT\displaystyle Q = mc\,\Delta T
Latent heat
Q=mL\displaystyle Q = mL

Heat transfer

Conduction
Qt=kA(T1−T2)L\displaystyle \frac{Q}{t} = \frac{kA(T_1 - T_2)}{L}
Stefan-Boltzmann law
P=eσAT4\displaystyle P = e\sigma A T^4
Wien's displacement law
λmT=b\displaystyle \lambda_m T = b
Newton's law of cooling
dTdt=−k(T−Ts)\displaystyle \frac{dT}{dt} = -k(T - T_s)

Where students slip up

  • Using Celsius in Stefan's law. T must be in kelvin.
  • Forgetting latent heat during a change of state. Temperature doesn't change while it melts or boils.
  • Using the wrong area in conduction, since it's the cross-section the heat flows through.

Try it on your weakest chapter.

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