Consider the following cyclic process carried out in two steps on a gas. Step 1: 50. J of heat is added to the gas, and 20. J of expansion work is performed. Step 2: 62 J of heat is removed from the gas as the gas is compressed back to the initial state. Calculate the work for the gas compression in Step 2.

The work for the gas compression is 32 J

Explanation:

Step 1: Data given

50 J of heat is added to the gas

20 J of expansion work

62 J of heat is removed from the gas as the gas is compressed back to the initial state

Step 2:

ΔE = q + w

⇒with q = 50 J of heat

⇒with w = 20 J of expansion work

 ⇒ expansion work = since there is work done by the gas: w is negative

ΔE = q + w

ΔE = 50 J - 20 J

ΔE = 30J

Step 3: Calculate the work for the gas compression

ΔE = -30 J = -62 J + w

⇒62 J of heat is removed from the gas as the gas is compressed back to the initial state. Compressed gas means work done by the surroundings => w is positive

⇒To go back to the initial state, we need 30 J

ΔE = -23 J

w = -30 J + 62 J = 32 J

The work for the gas compression is 32 J