A gas-turbine power plant operating on the simple Brayton cycle has a pressure ratio of 7. Air enters the compressor at 0°C and
100 kPa. The maximum cycle temperature is 1500 K. The compressor has an isentropic efficiency of 80 percent, and the turbine has an isentropic efficiency of 90 percent. Assume constant properties for air at 300 K with cv = 0.718 kJ/kg·K, cp = 1.005 kJ/kg·K, R = 0.287 kJ/kg·K, and k = 1.4.a) sketch the T-s diagram for the cycle.
b) if the net power output is 150 MW, determine the volume flow rate of the air into the compressor, in m^3/s.
c) for a fixed compressor inlet velocity and flow area, explain the effect of increasing compressor inlet temperature (i.e., summertime operation versus wintertime operation) on the inlet mass flow rate and the net power output with all other parameters of the problem being the same.
b) if the net power output is 150 MW, determine the volume flow rate of the air into the compressor, in m^3/s.
c) for a fixed compressor inlet velocity and flow area, explain the effect of increasing compressor inlet temperature (i.e., summertime operation versus wintertime operation) on the inlet mass flow rate and the net power output with all other parameters of the problem being the same.
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Answer:
Explanation:
<u>Given:</u>
= initial velocity of the electron =
= final velocity of the electron =
= initial position of the electron from the proton = very distant =
<u>Assume:</u>
= mass of an electron =
= magnitude of charge on an electron =
= magnitude of charge on an proton =
= Boltzmann constant =
= final position of the electron from the proton
= change in kinetic energy of the electron
= work done by the electrostatic force
= electrostatic force
= instantaneous distance of the electron from the proton
Let us first calculate the work done by the electrostatic force.
Using the principle of the work-energy theorem,
As only the electrostatic force is assumed to act between the two charges, the kinetic energy change of the electron will be equal to the work done by the electrostatic force on the electron due to proton.
Hence, the electron is at a distance of when the electron instantaneously has speed of three times the initial speed.