Find the amount of work done to increase the temperature of one mole of an ideal gas by 30 c if it is expanding under the condition vt2/3
Answers
Find the amount of work done to increase the temperature of one mole of an ideal gas by 30 c if it is expanding. .......We know that the formula for the work done in polytropic process P*V^(n) = K’ where K is constant and n is polytropic index is given by (P1*V1 - P2*V2)/(n - 1). Now P*V^(n) can be expressed in terms of T and V as T*V^(n-1) = K’’ (where K’’=K’/n*R) by substituting P from ideal gas equation PV = nRT. Now reducing the relation given in question in the above form we get T*V^(-3/2) = K. Comparing above two equation we can obtain the value of n as -(1/2). Now the work done in the polytropic process can also be given as n*R*( T1 - T2 )/(n - 1). We know the value of R, temperature difference, n and assuming for one mole of gas we can substitute the values in the equation and solve for the work.
W = (1*8.314*30) / ( -3 / 2) = - 166.28 kJ (Assuming temperature is decreased by 30)