At a power plant that produces 1 GW109 watts) of electricity, the steam turbines take in steam at a temperature of 500o, and the waste heat is expelled into the environment at 20o(a) What is the maximum possible efficiency of this plant?(b) Suppose you develop a new material for making pipes and turbines, which allows the maximum steam temperature to be raised to 600o. Roughly how much money can you make in a year by installing your improved hardware, if you sell the additional electricity for 5 cents per kilowatt-hour? (Assume that the amount of fuel consumed at the plant is unchanged.)
a) Maximum possible efficiency of the plant = 62.1%
b) Money can be made in a year $ 30 million
Temp at cold reservoir = 20o C and
Temp at hot reservoir = 500o
Convert temp in K.
Tc =20o C = 273+20= 193 K
Th =500oC = 273+500=773 K
The efficiency of power plant is given as
Maximum efficiency in percentage is 62.1%
The temperature of the cold reservoir = 20oThe temperature of the hot reservoir = 600oThe power plant produces 109 watts of electricity that is 109 J/s.Rate of additional electricity is 5 cents /kwh.
Th=600o=873 K and Tc=20o=293 K
Percentage of improved efficiency
With the improved efficiency the amount of electricity produced is
If sold for 5 cents per kilo-watt-hour then the money made in one second is:
Money made in one year is
=97.083 x 3600 x 24 x 365 cents
covert in $
= $ 30 Million ( approx)
Under many conditions, the rate at which heat enters an air conditioned building on a hot summer day is proportional to the difference in temperature between inside and outside, . (If the heat enters entirely by conduction, this statement will certainly be true. Radiation from direct sunlight would be an exception.) Show that, under these conditions, the cost of air conditioning should be roughly proportional to the square of the temperature difference. Discuss the implications, giving a numerical example.
Calculate the efficiency of a Rankine cycle that is modified from the parameters used in the text in each of the following three ways (one at a time), and comment briefly on the results:
(a) reduce the maximum temperature to 500oC;
(b) reduce the maximum pressure to 100 bars;
(c) reduce the minimum temperature to 10oC.
Suppose that the throttling valve in the refrigerator of the previous problem is replaced with a small turbine-generator in which the fluid expands adiabatically, doing work that contributes to powering the compressor. Will this change affect the COP of the refrigerator? If so, by how much? Why do you suppose real refrigerators use a throttle instead of a turbine?
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