Physics of Everyday Phenomena
Physics of Everyday Phenomena
9th Edition
ISBN: 9781259894008
Author: W. Thomas Griffith, Juliet Brosing Professor
Publisher: McGraw-Hill Education
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Chapter 11, Problem 5SP

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)

Expert Solution
Check Mark
To determine

The Carnot efficiency.

Answer to Problem 5SP

The Carnot efficiency is 35.5%.

Explanation of Solution

Given info:

Temperature of hot reservoir is 740°C and temperature of cold reservoir is 380°C.

Write an expression to calculate the efficiency.

η=1TCTH

Here,

η is the efficiency of the Carnot engine

TC is the temperature of cold reservoir

TH is the temperature of hot reservoir

Substitute 380°C for TC and 740°C for TH to find η.

η=1(380+273)K(740+273)K=0.355=(0.355)(100%)=35.5%

Thus, the Carnot efficiency is 35.5%.

Conclusion:

The Carnot efficiency is 35.5%.

(b)

Expert Solution
Check Mark
To determine

The efficiency of the actual oil-fired turbines.

Answer to Problem 5SP

The efficiency of the actual oil-fired turbines is 28.4%.

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.

η'=80%η

Here,

η' is the efficiency of the oil-fired power plant.

Substitute 0.355 for η to find η'.

W=(80%)(0.355)=28.4%

Thus, the efficiency of the actual oil-fired turbines is 28.4%.

Conclusion:

The efficiency of the actual oil-fired turbines is 28.4%.

(c)

Expert Solution
Check Mark
To determine

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 125000kWh.

Explanation of Solution

Given info:

The power of the oil-fired power plant is 125MW and the time is 1h.

Write an expression for electrical energy generated by the plant in one hour.

E=Pt

Here,

E is the energy

P is the energy

t is the energy

Substitute 125MW for P and 1h for t to find E.

E=(125MW)(103kW1MW)(1h)=125000kWh

Thus, the electrical energy generated by the plant in one hour is 125000kWh.

Conclusion:

The electrical energy generated by the plant in one hour is 125000kWh.

(d)

Expert Solution
Check Mark
To determine

The heat obtained from oil in each hour.

Answer to Problem 5SP

The heat obtained from oil in each hour is 440000kWh.

Explanation of Solution

Write an expression for efficiency of the actual oil-fired turbines.

E'=Eη'

Here,

E' is the heat obtained from oil in each hour.

Substitute 0.284 for η' and 1.25×105kWh for E to find η'.

E'=1.25×105kWh0.284=440000kWh

Thus, the heat obtained from oil in each hour is 440000kWh.

Conclusion:

The heat obtained from oil in each hour is 440000kWh.

(e)

Expert Solution
Check Mark
To determine

The amount of oil required to produce 1700kWh in each hour.

Answer to Problem 5SP

The amount of oil required to produce 1700kWh in each hour is 259 barrels of oil.

Explanation of Solution

Given info:

The energy released is 1700kWh.

Write an expression for the amount of oil required to produce 1700kWh in an hour.

n=E'Eh

Here,

E' is the energy released per hour

Eh is the energy released from one barrel oil per hour

n is the  amount of oil required to produce 1700kWh in an hour

Substitute 4.40×105kWh for E' and 1700kWh for Eh to find n.

n=4.40×105kWh1700kWh/barrel=259barrels

Thus, the amount of oil required to produce 1700kWh in each hour is 259 barrels of oil

Conclusion:

The amount of oil required to produce 1700kWh in each hour is 259 barrels of oil.

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Chapter 11 Solutions

Physics of Everyday Phenomena

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