Question

3 moles of an ideal gas are contained within a
cylinder by a frictionless piston and are initially at
temperature T. The pressure of the gas remains
constant while it is heated and its volume
doubles. If R is molar gas constant, the work done
by the gas in increasing its volume is
(1) 3/2RTIn2
(2) 3 RT In 2
(3) 3/2RT
(4) 3 RT​

Answer 1

Answer:

3RT (Option-4)

Explanation:

We know that,

work done at constant pressure , W=(P)x(V2-V1)

We know, PV=NRT

P=NRT/V

W=(NRT)(2V-V)/V

W=(NRT)(1)

Here,N=3

Therefore, W=3RT.

Answer 2

The work done by the gas in increasing its volume is 3RT

Explanation:

Number of moles of an ideal gas=n=3

Let P be the constant pressure of the gas

Let Initial volume of gas=$V_i=V$

Final volume of gas=$V_f=$2V

Change in volume=2V-V=V

Molar gas constant=R

Work done=$P\Delta V$

Where P=Constant pressure

$\Delta V$ =Change in volume

We know that

$P=\frac{nRT}{V}$

Work done=$\frac{nRT}{V}\times \Delta V$

Substitute the values then we get

Work done=$\frac{3RT\times V}{V}=3RT$

Option (4) is true.

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