# find the amount of work done to increase the temperature of one mole ideal gas by 30 degree if it is expanding under the condition V directly proportional to T^3/2

Vikas TU
14149 Points
11 years ago

Under the condition V directly proportional to T^3/2

we get, TV-2/3 = k2/3 (constant)

Relating from the eqn. TVY-1  = K0 (CONSTANT)

Y - 1 = - 2/3

Y = 1 - 2/3

Y = 1/3   [: - Y = Cv/Cp]

Now, W  = (nRT)/(1-Y)

pUTTING ALL THE VALUES =  1.R.30/(1 - 1/3)

= (30R)/(2/3)

=45R

=375 J.

Plz Approve

plz approve

plz approve

Arnav singh
13 Points
5 years ago
V proportional to T^2/3 , so
VT^-2/3= C(constant)
TV^-3/2=C'(some other constant)
Now as TV^Y-1 =C ,therefore
Y-1= -3/2
Y=-1/2
Now , W= nR∆T/1-Y => 1.8.314.30/ 1+1/2
=>1.8.314.30.2/3=> 166.28 J
Rishi Sharma
4 years ago
Dear Student,

V proportional to T^2/3 , so
VT^-2/3= C(constant)
TV^-3/2=C'(some other constant)
Now as TV^Y-1 =C ,therefore
Y-1= -3/2
Y=-1/2
Now , W= nR∆T/1-Y => 1.8.314.30/ 1+1/2
=>1.8.314.30.2/3=> 166.28 J

Thanks and Regards