what is the ratio of molar specific heat capacity of monoatomic gas
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Answer:
The molar specific heat capacity of a gas at constant volume (Cv) is the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant volume. Its value for monatomic ideal gas is 3R/2 and the value for diatomic ideal gas is 5R/2.
The molar specific heat of a gas at constant pressure (Cp) is the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure. Its value for monatomic ideal gas is 5R/2 and the value for diatomic ideal gas is 7R/2.
MonatomicDiatomicf35Cv3R/25R/2Cp5R/27R/2γγ1.671.40
The specific heat at constant volume is related to the internal energy UU of the ideal gas byCv=dUdT∣∣∣v=f2R,Cv=dUdT|v=f2R,where ff is degrees of freedom of the gas molecule. The degrees of freedom is 3 for monatomic gas and 5 for diatomic gas (3 translational + 2 rotational). The internal energy of an ideal gas at absolute temperature TT is given by U=fRT/2U=fRT/2.
The specific heat at constant pressure (Cp) is greater than that at constant volume (Cv). The heat given at constant volume is equal to the increase in internal energy of the gas. The heat given at constant pressure is equal to the increases in internal energy of the gas plus the work done by the gas due to increase in its volume (Q=ΔU+ΔWQ=ΔU+ΔW). The difference between CpCp and CvCv is given by Mayer's formulaCp−Cv=R.Cp−Cv=R.
The ratio of the specific heats, also called adiabatic index, is given byγ=CpCv=1+2f.γ=CpCv=1+2f.The ratio of the specific heats is 5/3 for monatomic ideal gas and 7/5 for diatomic gas. Its value for air is 1.4. This ratio is used to define (1) adiabatic process pVγ=constpVγ=const, and (2) speed of sound in gases v=√γRT/Mv=γRT/M.
Explanation:
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