# Carnot Heat Engine

## Homework Statement

Consider a Carnot engine that operates between a hot reservoir at 63°C and a cold reservoir at -14°C. In running 25 minutes, this engine absorbs 590 J of heat from the hot reservoir.

How much heat does it expel to the cold reservoir?

## Homework Equations

$$Q_H/Q_C = T_H/T_C$$

## The Attempt at a Solution

$$T_H = 336k$$
$$T_C = 287k$$
$$Q_H/Q_C = T_H/T_C \longrightarrow 590/Q_C = 336/287$$
Solving for $$Q_C$$ I get 504 J, however, this is not the correct answer. What am I missing?