A steam turbine operates between hot and cold reservoir temperatures of 538 degrees celcius and 92.1 degrees celcius respectively. If heat is supplied at a rate of 238 MW, what maximum amount of power could the turbine deliver?
To find the maximum amount of power that the steam turbine could deliver, we need to use the concept of Carnot efficiency. The Carnot efficiency is the maximum efficiency that any heat engine can achieve when operating between two temperatures.
The Carnot efficiency (η) is given by the formula:
η = 1 - (Tc/Th)
where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
In this case, Tc = 92.1 degrees Celsius and Th = 538 degrees Celsius.
Converting these temperatures to Kelvin:
Tc = 92.1 + 273.15 = 365.25 K
Th = 538 + 273.15 = 811.15 K
Now we can calculate the Carnot efficiency:
η = 1 - (365.25/811.15)
= 0.549
The Carnot efficiency represents the fraction of heat that can be converted into useful work. Therefore, the maximum amount of power that the turbine could deliver is equal to the product of the heat supplied and the Carnot efficiency:
Maximum power = heat supplied * Carnot efficiency
Converting the heat supplied to kilowatts (kW):
Heat supplied = 238 MW = 238,000 kW
Maximum power = 238,000 kW * 0.549
= 130,862 kW
Therefore, the maximum amount of power that the steam turbine could deliver is 130,862 kW.