Consider a P-V diagram in which the path followed by one mole of perfect gas in a cylindrical container is shown in Fig. 12.9.(a) Find the work done when the gas is taken from state 1 to state 2.(b...

Question

Consider a P-V diagram in which the path followed by one mole of perfect gas in a cylindrical container is shown in Fig. 12.9.
(a) Find the work done when the gas is taken from state 1 to state 2.

(b) What is the ratio of temperature T₁/T₂, if V₂ = 2V₁?

(c) Given the internal energy for one mole of gas at temperature T is (3/2) RT, find the heat supplied to the gas when it is taken from state 1 to 2, with V₂ = 2V₁.

Philoid · Accepted 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

C_v= Specific heat capacity at constant volume.

= Change in temperature

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

W=

AlsoV₂ = 2V₁

W=

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

Since, and n=1

Putting the value in equation 3

W=

Now,