# Specific Heat

## Specific Heat is the amount of heat required to change a unit mass of a substance by one degree in temperature

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Specific Heat is the amount of heat required to change a unit mass of a substance by one degree in temperature. The heat supplied to a mass can be expressed as

dQ = m c dt (1)

where

dQ = heat supplied (kJ, Btu)

m = unit mass (kg, lb)

c = specific heat (kJ/kg^{ o}C,kJ/kg^{ o}K,Btu/lb^{ o}F)

dt = temperature change (K,^{o}C,^{o}F)

*(1)* can be transferred to express Specific Heat as:

c = dQ / m dt (1b)

### Converting between commonly used Units

*1 Btu/lb*_{m}^{o}F = 4186.8 J/kg K = 1 kcal/kg^{o}C

#### Example - Heating Aluminum

*2 kg* of aluminum is heated from *20 ^{o}C* to

*100*. Specific heat of aluminum is

^{o}C*0.91 kJ/kg*and the heat required can be calculated as

^{0}C*dQ = (2 kg) (0.91 kJ/kg ^{0}C) ((100 ^{o}C) - (20 ^{o}C)) *

* = 145.6 (kJ)*

#### Example - Heating Water

*One liter* of water is heated from *0 ^{o}C* to boiling

*100*. Specific heat of water is

^{o}C*4.19 kJ/kg*and the heat required can be calculated as

^{0}C*dQ = (1 litre) (1 kg/litre) (4.19 kJ/kg ^{0}C) ((100 ^{o}C) - (0 ^{o}C)) *

* = 419 (kJ)*

### Specific Heat Gases

There are two definitions of Specific Heat for vapors and gases:

c_{p}= (δh / δT)_{p}- Specific Heat at constant pressure (kJ/kg^{o}C)

c_{v}= ( δh / δT)_{v}- Specific Heat at constant volume (kJ/kg^{o}C)

### Gas Constant

The gas constant can be expressed as

R =c_{p}- c_{v}(2)

where

R = Gas Constant

### Ratio of Specific Heat

The Ratio of Specific Heat is expressed as

k =c_{p}/ c_{v}(3)

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