IIT JEE , AIEEE Forum - Physics , Thermal Physics

pottermania1990

1)an ideal gas is taken through a process in which the pressure and volume are related as p=kv.show that molar heat capacity of the gas for the process is given by c = Cv + R/2

(Cv - molar heat capacity at constant volume)

2)an ideal gas with Cp/Cv =

is taken through a process in which pressure and volume vary as p = av^b..find the value of b for which the specific heat capacity for the process is zero..

please post with complete solutions

anchitsaini

p=kv
w=integ(pdv)
=kv^2/2
=pv/2
for one mole n=1
therefore pv=rt
so w=rt/2

and the first law of thermodynamics--
dQ=dU+dW
is also
C t=Cv t +w
therefore
Ct=Cvt + rt/2
therefore
C=Cv +r/2

anchitsaini

p=av^b
therefore
w=integ pdv
=integ a v^b dv
=(a v^b+1)/(b+1)
=pv/(b+1)
=Rt/(b+1)

Cv=R/y-1
C t=Cv t + Rt/(b+1)
=0
therefore
R/y-1+aR/b +1=0
b+1+(y-1)=0
b=-y
i have done calc on comp so do tell me if i'm wrong

iitkgp_bipin

Good work Anchit.

For a process : PV^x = constant

molar heat capacity, C = C_v + R/(1-x)

for the first problem : PV^-1 = k, so put x = -1 to obtain C.

2nd problem : PV^-b = k, so x = -b

C = C_v + R/(1-(-b)) = 0 (given)

so, b = -R/C_v - 1

as we know C_v = R/(

-1)

b = -(

-1) - 1

b = -

pottermania1990

thanx bipin and anchit

Ask & Discuss Questions with Community & Experts