Question

Question:A Carnot engine has an efficiency of 66% and performs\({\bf{2}}{\bf{.5 \times 1}}{{\bf{0}}^{\bf{4}}}\;{\bf{J}}\)of work in each cycle. (a) How much heat does the engine extract from its heat source in each cycle? (b) Suppose the engine exhausts heat at room temperature (20.0°C). What is the temperature of its heat source?

Short answer

The heat extracted by engine from heat source is \(38\;{\rm{kJ}}\).

Step-by-step solution

Identification of given data

The efficiency of Carnot engine is\(\eta = 0.66\)

The work done in each cycle is\(W = 2.5 \times {10^4}\;{\rm{J}}\)

The temperature of room is \(T = 20\;^\circ {\rm{C}}\)

Conceptual Explanation

The heat extracted by the engine from heat source is calculated by using the formula of thermal efficiency.

Determination of heat extracted by engine from heat source

The heat extracted by engine from heat source is given as:

\(\eta = 1 - \frac{W}{Q}\)

Substitute all the values in the above equation.

\(\begin{array}{l}0.66 = \frac{{2.5 \times {{10}^4}\;{\rm{J}}}}{Q}\\Q = 3.78 \times {10^4}\;{\rm{J}}\\Q = \left( {3.78 \times {{10}^4}\;{\rm{J}}} \right)\left( {\frac{{1\;{\rm{kJ}}}}{{{{10}^3}\;{\rm{J}}}}} \right)\\Q \approx 38\;{\rm{kJ}}\end{array}\)

Therefore, the heat extracted by engine from heat source is \(38\;{\rm{kJ}}\).