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.)
b) $ 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
Substitute the values we get
In percentage it is 62.1%
The temperature of the cold reservoir = 20o
The 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 == 66.44% ( rounding)
With the improved efficiency the amount of electricity produced is
So additional 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)
Consider an ideal Hampson-Linde cycle in which no heat is lost to the environment.
(a) Argue that the combination of the throttling valve and the heat exchanger is a constant-enthalpy device, so that the total enthalpy of the fluid coming out of this combination is the same as the enthalpy of the fluid going in.
(b) Let be the fraction of the fluid that liquefies on each pass through the cycle. Show that
where is the enthalpy of each mole of compressed gas that goes into the heat exchanger, is the enthalpy of each mole of low-pressure gas that comes out of the heat exchanger, and is the enthalpy of each mole of liquid produced.
(c) Use the data in Table to calculate the fraction of nitrogen liquefied on each pass through a Hampson-Linde cycle operating between 1 bar and 100 bars, with an input temperature of . Assume that the heat exchanger works perfectly, so the temperature of the low-pressure gas coming out of it is the same as the temperature of the high-pressure gas going in. Repeat the calculation for an input temperature of .
Suppose you are told to design a household air conditioner using
HFC-134a as its working substance. Over what range of pressures would you have it operate? Explain your reasoning. Calculate the COP for your design, and compare to the COP of an ideal Carnot refrigerator operating between the same extreme temperatures.
The amount of work done by each stroke of an automobile engine is controlled by the amount of fuel injected into the cylinder: the more fuel, the higher the temperature and pressure at points 3 and 4 in the cycle. But according to equation 4.10, the efficiency of the cycle depends only on the compression ratio (which is always the same for any particular engine), not on the amount of fuel consumed. Do you think this conclusion still holds when various other effects such as friction are taken into account? Would you expect a real engine to be most efficient when operating at high power or at low power? Explain.
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