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, givenV_{2} = 2V_{1}

c.

Where, is change in internal energy given by

n = No. Of moles

C_{v}= Specific heat capacity at constant volume.

= Change in temperature

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

W=

AlsoV_{2} = 2V_{1}

W=

W=

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

Since, and n=1

Putting the value in equation 3

W=

Now,

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