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Specific Heat or Specific Heat Capacity

Specific heat characterizes the nature of the substance in response to the heat supplied to the substance.

Molar specific heat

The molar specific heat of a substance may be defined as the amount of heat required to raise the temperature of one gram mole of a substance by a unit degree. It is represented by capital (C).
 
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Units: 57551.png57544.png

 

Important Points
  • 58080.png58074.png
     
    i.e., the molar specific heat of a substance is M times the gram specific heat, where M is the molecular weight of that substance.
  • Specific heat also depends on the conditions of the experiment i.e., the way in which heat is supplied to the body. In general, experiments are made either at constant volume or at constant pressure.

Specific heat of gases

In case of gases, the heat energy supplied to a gas is spent not only in raising the temperature of the gas but also in the expansion of gas against atmospheric pressure. Hence, specific heat of a gas, which is the amount of heat energy required to raise the temperature of 1 g of gas through a unit degree, shall not have a single or unique value.
  • If the gas is compressed suddenly and no heat is supplied from outside, i.e., ΔQ = 0, but the temperature of the gas raises on the account of compression
     
    ∴ 57513.png ⇒ C = 0
  • If the gas is heated and allowed to expand at such a rate that rise in temperature due to heat supplied is exactly equal to fall in temperature due to expansion of the gas, i.e., ΔT = 0
     
    57507.png ⇒ C = ∞
  • If the rate of expansion of the gas were slow, the fall in temperature of the gas due to expansion would be smaller than the rise in temperature of the gas due to heat supplied. Therefore, there will be some net rise in temperature of the gas, i.e., ΔT will be positive.
     
    57501.png positive  C = positive
  • If the gas were to expand very fast, fall of temperature of gas due to expansion would be greater than rise in temperature due to heat supplied. Therefore, there will be some net fall in temperature of the gas, i.e., ΔT will be negative.
     
    57495.pngnegative  C = negative
Hence, the specific heat of gas can have any positive value ranging from zero to infinity. Further it can even be negative. The exact value depends upon the mode of heating the gas. Out of many values of specific heat of a gas, two are of special significance.
 
Specific heat of a gas at constant volume (cv) The specific heat of a gas at constant volume is defined as the quantity of heat required to raise the temperature of unit mass of gas through 1 K when its volume is kept constant, i.e.,
 
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If instead of unit mass, 1 mole of gas is considered, the specific heat is called molar specific heat at constant volume and is represented by capital Cv.
 
57482.png57476.png
 
Specific heat of a gas at constant pressure (cpThe specific heat of a gas at constant pressure is defined as the quantity of heat required to raise the temperature of unit mass of gas through 1 K when its pressure is kept constant, i.e.,
 
57470.png
 
If instead of unit mass, 1 mol of gas is considered, the specific heat is called molar specific heat at constant pressure and is represented by Cp i.e.,
 
57464.png57458.png
 
Mayer’s formula 57452.png
This relation is called Mayer’s formula and shows that Cp > Cv, i.e., molar specific heat at constant pressure is greater than that at constant volume.
 
Specific heat in terms of degree of rreedom
 
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Important Points
  • Value of γ is always more than 1. So we can say that always Cp > Cv.
  • Value of γ is different for monoatomic, diatomic, and triatomic gases.
  • As 58059.png 58052.png
     
    ∴ 58046.png
     
    and 58040.png58033.png




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