Specific Heat

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The 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 unit 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 ^oC, kJ/kg ^oK, Btu/lb ^oF)

dt = temperature change (K, ^oC, ^oF)

Expressing Specific Heat using (1)

c = dQ / m dt         (1b)

Converting between Common Units

• 1 Btu/lb_m^oF = 4186.8 J/kg K = 1 kcal/kg^oC

Example - Heating Aluminum

2 kg of aluminum is heated from 20 ^oC to 100 ^oC. Specific heat of aluminum is 0.91 kJ/kg⁰C and the heat required can be calculated as

dQ = 2 (kg) 0.91 (kJ/kg⁰C) (100 (^oC) - 20 (^oC)) 

     = 145.6 (kJ)

Example - Heating Water

One litre of water is heated from 0 ^oC to boiling 100 ^oC. Specific heat of water is 4.19 kJ/kg⁰C and the heat required can be calculated as

dQ = 1 (litre) 1 (kg/litre) 4.19 (kJ/kg⁰C) (100 (^oC) - 0 (^oC)) 

     = 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^oC)

c_v = ( δh/ δT)_v - Specific Heat at constant volume (kJ/kg^oC)

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

k = c_p / c_v         (3)

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Related Topics

• Thermodynamics - The effects of work, heat and energy on a system

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