Question
Sat April 28, 2012 By: Amit Das

How is the molar specific heat capacity of nitrogen at constant pressure calculated? Please explain in detail.

Expert Reply
Wed May 09, 2012
specific heat capacity at constant pressure = dU-W / m. dT

dU = change in internal energy 
W = work done
m = mass of gas
dT = change in temperature 
 
The internal energy of the gas increases by adding heat Q to it and/or doing positive work W on it: dU=Q+W. At constant volume, the work is zero, so Q=dU =n Cv dT. At constant pressure, the gas does work of PdV while taking heat on, so more heat is needed to rise its temperature. Cp is the heat which rises the temperature of 1mol gas by 1 K. At constant pressure dU=Q-PdV=nCp dT-PdV. As PV=nRT, dU=nCpdT-nRdT=n dT(Cp-R). But dU=n Cv dT, so Cp=Cv+R for an ideal gas.

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