Joule conversion Heat+Work First Law

Question

An automobile engine generates 2220 Joules of heat that must be carried away by the cooling system. The internal energy changes by -2856 Joules in this process.

What is w for the engine? This represents the amount of work available to push the pistons in this process.

w =  Joules

Answer 1

Change in internal energy = ∆U = q + w

Given:

q = -2220 J (negative because heat is generated by the system, i.e. exothermic)

∆U = -2856 J

Asked for w:

-2856 J = -2220 J + w

w = -636 J (note work is negative because work is being done BY the system ON the surroundings)

Answer 2

We have to use the second law of thermodynamics:

dQ=dU+dW

dW=dQ-dU

dW=2220-(-2856)=5076 J