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 :

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) $$-$$ $${{1 \over 2}}$$]

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

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