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 in step 2 = 32 J

Explanation:

Given that:

A system usually comes back to initial state after 2 steps;

That implies:

ΔE₁ + ΔE₂ = 0

When heat is added to a given system, q tends to be positive

q is also negative when the heat is removed from the system

The work (W) when expansion occurs is said to be negative and positive when compression occurs.

∴ ΔE₁ = q₁ + W₁

ΔE₁ = 50 J + (-20 J)

ΔE₁ = 30 J

ΔE₂ = q₂ + W₂

ΔE₂ = - 62 J + W₂

ΔE₁ + ΔE₂ = 0

30 J - 62 J + W₂ = 0

W₂ = - 30 J + 62 J

W₂ = 32 J

Thus, the work for the gas compression in step 2 = 32 J