Question 346: Thermodynamics & KTG

Question

n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.
A $ 	o $ B : Isothermal expansion at temperature T so that the volume is doubled from V
1
to V
2
= 2V
1
and pressure charges from P
1
to P
2
B $ 	o $ C : Isobaric compression at pressure P
2
to initial volume V
1
.
C $ 	o $ A : Isochoric change leading to change of pressure from P
2
to P
1
.
Total workdone in the complete cycle ABCA is :
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l9fnkpbb/dca5bfac-42c1-4754-98b6-1586ed04de86/83d13370-4faf-11ed-88d9-abb495ae8a3e/file-1l9fnkpbc.png?format=png)

Accepted Answer

A $ 	o $ B = isothermal process
B $ 	o $ C = isobaric process
C $ 	o $ A = isochoric process
also, V
2
= 2V
1
work done by gas in the complete cycle ABCA is -
$ \Rightarrow $ w = w
AB
+ w
BC
+ w
CA
.....(1)
$ \Rightarrow $ w
CA
= 0, as isochoric process
$ \Rightarrow $ w
AB
= 2P
1
V
1
ln$\left( {{{{v_2}} \over {{v_1}}}} ight)$ = 2 nRT ln(2)
$ \Rightarrow $ w
BC
= P
2
(V
1
$-$ V
2
) = P
2
(V
1
$-$ 2V
1
) = $-$P
2
V
1
= $-$nRT
$ \Rightarrow $ Now put the value of w
AB
, w
BC
and w
CA
in equation, we get
$ \Rightarrow $ w = 2nRT ln(2) $-$ nRT + 0
$ \Rightarrow $ w = nRT [2ln (2) $-$ 1]
$ \Rightarrow $ w = nRT [ln (2) $-$ ${{1 \over 2}}$]
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l9fnkpbb/dca5bfac-42c1-4754-98b6-1586ed04de86/83d13370-4faf-11ed-88d9-abb495ae8a3e/file-1l9fnkpbc.png?format=png)

Answer

nRTln 2

Answer

0

Answer

$nRT\left( {\ln 2 - {1 \over 2}} \right)$

Answer

$nRT\left( {\ln 2 + {1 \over 2}} \right)$

Thermodynamics & KTG

Choose the correct answer: