Answer to Question #123079 in Molecular Physics | Thermodynamics for vamsi

Question #123079
The temperature of n moles of ideal gas is increased from T to 4T through a process for which pressure P = a T^(-1) ,where 'a' is a constant. The work done by the gas is ?
1
Expert's answer
2020-06-21T20:01:52-0400

Change in temperature is ,ΔT=4TT=3TΔT=4T−T=3T

Given, gas obeys the law

P=aT1P=aT^{-1}

Now, from ideal gas law, PV=nRTPV=nRT

and solving the above equation we get,

PV12=constantPV^{\frac{1}{2}}=constant

Thus, process is poly-tropic.

We, know that molar heat capacity is

C=Cv+R1xC=C_v+\frac{R}{1-x}

​Hence,

C=Cv+2RC=C_v+2R

Now, we also know that, heat absorbed is

ΔQ=nCΔT=ΔU+ΔW=nCvΔT+ΔWΔQ=nCΔT=ΔU+ΔW=nC_v\Delta T+\Delta W

Therefore, we get, work done is

ΔW=nΔT(CCv)=6nRT\Delta W=n\Delta T(C-C_v)=6nRT

Note: RR is universal gas constant.


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