Consider the following cyclic process carried out in two steps on a gas.
Step 1: 35 J of heat is added to the gas, and 12 J of expansion work is performed.
Step 2: 65 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. J

The work for the gas compression is 42 J

Explanation:

Step 1: Data given

35 J of heat is added to the gas

12 J of expansion work

65 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 = 35 J of heat

⇒with w = 12 J of expansion work

  ⇒ expansion work = work done by the gas = w is negative

ΔE = 35 J - 12 J

ΔE = 23 J

Step 3: Calculate the work for the gas compression

ΔE = -23 J = -65 J + w

⇒65 J of heat is removed from the gas as the gas is compressed back to the initial state

⇒ We need 23 J to go back to the initial state: ΔE = -23 J

Compressed gas means work done by the surroundings => w is positive

w = -23 J + 65 J = 42 J

The work for the gas compression is 42 J