Question

7. A cylinder containing the air comprises the system. Cycle is completed as

follows :

(i) 82000 N-m of work is done by the piston on the air during compression stroke and

45 kJ of heat are rejected to the surroundings.

(ii) During expansion stroke 100000 N-m of work is done by the air on the piston.

Calculate the quantity of heat added to the system.

Answer 1

Compression stroke. Process 1-2 :

Work done by the piston on the air, $W_{1–2} = – 82000 \;Nm\; (= – 82 \;kJ)$

Heat rejected to the system,

$Q_{1–2} = – 45 \;kJ \\ Q_{1–2} = (U_2 - U_1 ) + W \\ – 45 = (U_2 - U_1 ) + (– 82) \\ (U_2-U_1) = 37 \;kJ$

Work done by air on the piston,

$W_{2–1} = 100000 \;Nm \;(= 100 \;kJ) \\ Q_{2–1} = (U_1 - U_2 ) + W \\ = – 37 + 100\; kJ = 63\; kJ$

Hence, quantity of heat added to the system = 63 kJ.