12.3 Introduction to the second law of thermodynamics: heat engines  (Page 6/10)

Imagine you are driving a car up Pike’s Peak in Colorado. To raise a car weighing 1000 kilograms a distance of 100 meters would require about a million joules. You could raise a car 12.5 kilometers with the energy in a gallon of gas. Driving up Pike's Peak (a mere 3000-meter climb) should consume a little less than a quart of gas. But other considerations have to be taken into account. Explain, in terms of efficiency, what factors may keep you from realizing your ideal energy use on this trip.

Is a temperature difference necessary to operate a heat engine? State why or why not.

Definitions of efficiency vary depending on how energy is being converted. Compare the definitions of efficiency for the human body and heat engines. How does the definition of efficiency in each relate to the type of energy being converted into doing work?

Why—other than the fact that the second law of thermodynamics says reversible engines are the most efficient—should heat engines employing reversible processes be more efficient than those employing irreversible processes? Consider that dissipative mechanisms are one cause of irreversibility.

A certain heat engine does 10.0 kJ of work and 8.50 kJ of heat transfer occurs to the environment in a cyclical process. (a) What was the heat transfer into this engine? (b) What was the engine’s efficiency?

With $2\text{.}\text{56}\times {\text{10}}^6\text{J}$ of heat transfer into this engine, a given cyclical heat engine can do only $1\text{.}\text{50}\times {\text{10}}^5\text{J}$ of work. (a) What is the engine’s efficiency? (b) How much heat transfer to the environment takes place?

(a) What is the work output of a cyclical heat engine having a 22.0% efficiency and $6\text{.}\text{00}\times {\text{10}}^9\text{J}$ of heat transfer into the engine? (b) How much heat transfer occurs to the environment?

(a) What is the efficiency of a cyclical heat engine in which 75.0 kJ of heat transfer occurs to the environment for every 95.0 kJ of heat transfer into the engine? (b) How much work does it produce for 100 kJ of heat transfer into the engine?

The engine of a large ship does $2\text{.}\text{00}\times {\text{10}}^8\text{J}$ of work with an efficiency of 5.00%. (a) How much heat transfer occurs to the environment? (b) How many barrels of fuel are consumed, if each barrel produces $6\text{.}\text{00}\times {\text{10}}^9\text{J}$ of heat transfer when burned?

(a) How much heat transfer occurs to the environment by an electrical power station that uses $1\text{.}\text{25}\times {\text{10}}^{\text{14}}\text{J}$ of heat transfer into the engine with an efficiency of 42.0%? (b) What is the ratio of heat transfer to the environment to work output? (c) How much work is done?

Assume that the turbines at a coal-powered power plant were upgraded, resulting in an improvement in efficiency of 3.32%. Assume that prior to the upgrade the power station had an efficiency of 36% and that the heat transfer into the engine in one day is still the same at $2\text{.}\text{50}\times {\text{10}}^{\text{14}}\text{J}$ . (a) How much more electrical energy is produced due to the upgrade? (b) How much less heat transfer occurs to the environment due to the upgrade?

This problem compares the energy output and heat transfer to the environment by two different types of nuclear power stations—one with the normal efficiency of 34.0%, and another with an improved efficiency of 40.0%. Suppose both have the same heat transfer into the engine in one day, $2\text{.}\text{50}\times {\text{10}}^{\text{14}}\text{J}$ . (a) How much more electrical energy is produced by the more efficient power station? (b) How much less heat transfer occurs to the environment by the more efficient power station? (One type of more efficient nuclear power station, the gas-cooled reactor, has not been reliable enough to be economically feasible in spite of its greater efficiency.)