Answer :

a. We know that work done is given by an ideal gas is given by,



According to question,




Work done by the gas=



...............(1)


Since ,


Putting the value equation 1 becomes,


Work done=


c. To relate the temperature we have to modify the equation in terms of T.


From ideal gas equation we know,


PV=nRT


Where,


P=pressure


V=volume


T=absolute temperature


n=number of moles of gas


R=ideal gas constant


Here, n=1 (given)



But ,


So, comparing both we get,



Or



=new constant=C



For state 1 let,


For state 2 let,


Equating both we get,




Now, givenV2 = 2V1




c.



Where, is change in internal energy given by


n = No. Of moles


Cv= Specific heat capacity at constant volume.


= Change in temperature




...........(2)


W=


AlsoV2 = 2V1


W=


W=


W= ............(3)


Since, and n=1



Putting the value in equation 3


W=


Now,








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