eguruchela

List of formulas related to changes of state and shape

Heat

Qe: Heat emitted, Qr: Heat received, m: object’s total mass(kg), c: specific heat(J/kg.K), Δt: change in temperature(K)

$$ \sum Q_c = \sum Q_r $$ $$ Q = mc \Delta t $$

The specific heats of some material

SubstanceSpecific Heat
(J/kg.K)
Water4200
Ice Water2100
Aluminium880
Iron460
Copper380
Lead130

Fusion(Freezing Or Solidification)


Q: quantity of heat(J), λ: heat of fusion(j/kg), m: mass(kg)

$$ Q = \lambda m $$

Heat Of Fusion Some Materials

SubstanceLatent Heat Of Melting
(J/kg)
Lead25
Tin60
Gold67
Mercury11
silver88
Iron209
Ice Water334
Aluminium321

Vaporization

L: heat of vaporization

$$ Q = L m $$

Heat Of Vaporization Of Some Materials

SubstanceHeat Of Vaporization
(J/kg)
Water2,26.106
Iron5,80.104
Mercury2,85.105
Wine8,57.105

Linear Expansion

Io: original length (m), α: coefficient of linear expansion(K), Δt: change in temperature

$$ l = l_o(1 + {\alpha} \Delta t) $$ $$ \Delta l = l_o \alpha \Delta t $$

Volume Expansion

$$ V = V_o (1 + \beta \Delta t) $$ $$ = V_o (1 + 3 \alpha \Delta t) $$ $$ \Delta V = V_o 3 \alpha \Delta t $$

Area Expansion

$$ S = S_o (1 + 2 \alpha \Delta t ) $$ $$ \Delta S = S. 2 \alpha \Delta t $$

Change Of Density(Volumetric Mass Density)

Do: original density (kg/m3)

$$ \frac{1}{D} = \frac{1}{D_o} (1 + 3 \alpha \Delta t) $$ $$ D = \frac{D_o} {1 + 3 \alpha. \Delta t } $$

Change Of Diameter Of The Cross Section Of A Solid

$$ d^2 = {d_o}^2 (1 + 2 \alpha \Delta t ) $$ $$ \Delta t = \frac{\frac {d^2}{d_o^2} - 1}{2 \alpha} $$