Question

calculate the value of Cp and Cv for monoatomic gas.why Cp is greater than Cv?

Answer 1

The value of Cp and Cv for a monoatomic gas is

Cp= (5/2) R and Cv = (3/2) R

Expression for Cp

Cp is the amount of heat capacity required to raise the temperature of substance by one degree at constant pressure. So we have

Q = nCpT

According to first law of thermodynamics we have:--

Q = E + W.....(1)  ( E is internal energy and W is work done)

At constant pressure W = P(V2-V1) = nRT

E =(3/2)nRT substituting value of E and W in equation (1)

Q = (3/2)nRT + nRT

So Q = (5/2)nRT and also Q = nCpT

so we have Cp =(5/2) R

Expression for Cv

Cv is the amount of heat required o raise temperature of body by one degree at constant volume. So we have

Q = nCvT

According to first law of thermodynamics we have;-

Q = E + W.......(2)   ( E is internal energy and W is work done)

At constant volume work done is 0 as change is volume is 0 so W=0

And E = 3/2 nRT substituting in (2) we have Q = (3/2) nRT

so Cv =(3/2) R

Cp is greater than Cv

Cp = (5/2) R and Cv= (3/2) R

So Cp-Cv = R

So Cp is greater than Cv and the difference is due to the work involved in changing the volume. At constant volume no external work is done, hence all heat provided to system is used to raise the internal energy of the system.

However at constant pressure there will be increase in volume of system as well as some external work is also done hence some extra heat is supplied to system at constant pressure.

Therefore heat at constant pressure (Cp) is greater than heat supplied at constant volume (Cv).

Answer 2

Answer:

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