Question

90 kJ of heat are supplied to a system at a constant volume. The system
rejects 95 kJ of heat at constant pressure and 18 kJ of work is done on it. The system is brought
to original state by adiabatic process. Determine :
(i) The adiabatic work ;
(ii) The values of internal energy at all end states if initial value is 105 kJ.

Answer 1

Gives

Heat supplied at constant volume=90kJ

Heat rejected=-95kJ

Work done=-18kJ

U_l=105kJ

Process constant volume (l- m)

W=0

Q=90

90=U_m-U_l

U_m=U_i+90

U_m=105+90=195kJ

Process is constant pressure (m- n)

Q=U_n-U_m+W_m-n

-95=U_n-U_m-18

U_n-Um=-77kJ

195-77=U_n

U_n=118KJ

adiabatic process

Q_n-l=0

$\smallint(∆Q)=90-95=-5KJ\\∆W=-18+W_{n-l}=-5\\W_{n-l}=-5+18=13KJ\\(a)W_{n-l}=13KJ\\(b)\\U_m=195KJ\\U_n=118KJ$