Question

One mole of a gas expands with temperature t such that its volume, v=kt2, where k is a constant. If the temperature of the gas changes by 60oc, then the work done by the gas is:

Answer 1

As per definition of W,

d W = P dV

d W = R T / V dV

d W = R T / KT ^ 2 / 3 ------ 1

As,  

V = KT ^ 2 / 3

By derivating,

dV = K 2 / 3 T ^ - 1/3 dT

By integration from T1 to T2 and putting the value in equation 1 :

W = 2 / 3 R  ∫ dT

W = 2 /3 R ( T2 - T1 )

W = 2 / 3 R x 60

W = 40 R