﻿ All the formulas related to Changes Of State And Shape

# 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

### 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)
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

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