Suppose that an oil-fired power plant is designed to produce 125 MW (megawatts) of electrical power. The turbine operates between temperatures of 740°C and 380°C and has an efficiency that is 80% of the ideal Carnot efficiency for these temperatures.
a. What is the Carnot efficiency for these temperatures?
b. What is the efficiency of the actual oil-fired turbines?
c. How many kilowatt-hours (kW·h) of electrical energy does the plant generate in 1 h? (The kilowatt-hour is an energy unit equal to 1 kW of power multiplied by 1 h.)
d. How many kilowatt-hours of heat must be obtained from the oil in each hour?
e. If one barrel of oil yields 1700 kW·h of heat, how much oil is used by the plant each hour?
(a)
The Carnot efficiency.
Answer to Problem 5SP
The Carnot efficiency is
Explanation of Solution
Given info:
Temperature of hot reservoir is
Write an expression to calculate the efficiency.
Here,
Substitute
Thus, the Carnot efficiency is
Conclusion:
The Carnot efficiency is
(b)
The efficiency of the actual oil-fired turbines.
Answer to Problem 5SP
The efficiency of the actual oil-fired turbines is
Explanation of Solution
Given info:
The efficiency of the oil-fired power plant is 80% of the efficiency of the Carnot efficiency.
Write an expression for efficiency of the actual oil-fired turbines.
Here,
Substitute
Thus, the efficiency of the actual oil-fired turbines is
Conclusion:
The efficiency of the actual oil-fired turbines is
(c)
The electrical energy generated by the plant in one hour.
Answer to Problem 5SP
The electrical energy generated by the plant in one hour is
Explanation of Solution
Given info:
The power of the oil-fired power plant is
Write an expression for electrical energy generated by the plant in one hour.
Here,
Substitute
Thus, the electrical energy generated by the plant in one hour is
Conclusion:
The electrical energy generated by the plant in one hour is
(d)
The heat obtained from oil in each hour.
Answer to Problem 5SP
The heat obtained from oil in each hour is
Explanation of Solution
Write an expression for efficiency of the actual oil-fired turbines.
Here,
Substitute
Thus, the heat obtained from oil in each hour is
Conclusion:
The heat obtained from oil in each hour is
(e)
The amount of oil required to produce
Answer to Problem 5SP
The amount of oil required to produce
Explanation of Solution
Given info:
The energy released is
Write an expression for the amount of oil required to produce
Here,
Substitute
Thus, the amount of oil required to produce
Conclusion:
The amount of oil required to produce
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Chapter 11 Solutions
Physics of Everyday Phenomena
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