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Chapter 15: 7MCQ (page 412)

A heat engine operates between a high temperature of about 600°C and a low temperature of about 300°C. What is the maximum theoretical efficiency for this engine?

(a) \( = 100\% \). (b) \( \approx 66\% \). (c) \( \approx 50\% \). (d) \( \approx 34\% \).

(e) Cannot be determined from the given information.

Short Answer

Expert verified

The correct option is (d).

Step by step solution

01

Concepts

The efficiency of the heat engine is \(e = 1 - \frac{{{Q_{\rm{L}}}}}{{{Q_{\rm{H}}}}}\).

The most used form of the efficiency of the heat engine is\(e = 1 - \frac{{{T_{\rm{L}}}}}{{{T_{\rm{H}}}}}\).

02

Given data 

The lower temperature is \({T_{\rm{L}}} = {300^ \circ }{\rm{C}} = 573\;{\rm{K}}\).

The higher temperature is \({T_{\rm{H}}} = {600^ \circ }{\rm{C}} = 873\;{\rm{K}}\).

03

Calculation 

Now, the efficiency of the heat engine is:

\(\begin{array}{c}e = \left( {1 - \frac{{{T_{\rm{L}}}}}{{{T_{\rm{H}}}}}} \right) \times 100\% \\ = \left( {1 - \frac{{573\;{\rm{K}}}}{{873\;{\rm{K}}}}} \right) \times 100\% \\ \approx 34\% \end{array}\)

Therefore, the efficiency of the heat engine is around \(34\% \).

Hence, the correct option is (d).

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Most popular questions from this chapter

(I) An ideal gas expands isothermally, performing\({\bf{4}}{\bf{.30 \times 1}}{{\bf{0}}^{\bf{3}}}\;{\bf{J}}\) of work in the process. Calculate (a) the change in internal energy of the gas, and (b) the heat absorbed during this expansion.

Two 1100 kg cars are traveling at a speed of\({\bf{85 km/h}}\)in opposite directions when they collide and are brought to rest. Estimate the change in entropy of the universe as a result of this collision. Assume\(T = {\bf{20\circ C}}\).

Question:(I) If an ideal refrigerator keeps its contents at 2.5°C when the house temperature is 22°C, what is its COP?

(I) One liter of air is cooled at constant pressure until its volume is halved, and then it is allowed to expand isothermally back to its original volume. Draw the process on a PV diagram.

An ideal gas undergoes an adiabatic expansion, a process in which no heat flows into or out of the gas. As a result,

(a) the temperature of the gas remains constant and the pressure decreases.

(b) both the temperature and pressure of the gas decrease.

(c) the temperature of the gas decreases and the pressure increases.

(d) both the temperature and volume of the gas increase.

(e) both the temperature and pressure of the gas increase
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