Air at 25°C and 100kPa flows to a isothermal reversible compressor. The compressor releases heat at a sufficient rate to the environment (also at 25°C) to ensure that the air at the outlet of the compressor is at 25°C. The air from the compressor flows to a rigid tank of 2m³. The tank is initialy filled with air at 100kPa and 25°C. The tank releases heat at a sufficient rate to the environment to ensure that the temperature of the air in the tank also remains on 25°C. The process continues until the pressure in the tank reaches 1000kPa. Calculate the power required by the compressor. All processes are reversible.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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where do thet get the enthropy valvue for S2?

Example
Air at 25°C and 100kPa flows to a isothermal reversible compressor. The compressor
releases heat at a sufficient rate to the environment (also at 25°C) to ensure that the air at
the outlet of the compressor is at 25°C. The air from the compressor flows to a rigid tank
of 2m³. The tank is initialy filled with air at 100kPa and 25°C. The tank releases heat at
a sufficient rate to the environment to ensure that the temperature of the air in the tank
also remains on 25°C. The process continues until the pressure in the tank reaches
1000kPa. Calculate the power required by the compressor. All processes are reversible.
Solution
An entropy and energy balance over the compressor alone cannot be used to solve the
problem as the value of entropy of the air at the outlet of the compressor is not constant,
it changes as the outlet pressure of the compressor rises.
Consider the whole system. (It is left to the reader to draw a picture.) An energy balance
gives:
m₁u₁ + mihi + Win = m₂u2 + Qtot
Where Qtot is the heat released by the compressor and the tank. We can determine m₁
and m₂ from the Ideal Gas Law and m; from a mass balance. We can read the values for
enthalpy and internal energy from the tables, but it still leaves two unknowns, the work
and heat transfer. However, as the process is reversible, the total entropy remains constant
and the entropy at the beginning plus entropy in = entropy at the end plus entropy out:
m181 + mįsi = m282 +
Qtot
Tair
The total amount of heat released can now be calculated:
Qtot = 298.15(2.337 × 6.863 +21.04 × 6.863 - 23.37 x 6.202) = 4606kJ
The energy balance can now be used to calculate the work required by the compressor:
2805kJ.
Transcribed Image Text:Example Air at 25°C and 100kPa flows to a isothermal reversible compressor. The compressor releases heat at a sufficient rate to the environment (also at 25°C) to ensure that the air at the outlet of the compressor is at 25°C. The air from the compressor flows to a rigid tank of 2m³. The tank is initialy filled with air at 100kPa and 25°C. The tank releases heat at a sufficient rate to the environment to ensure that the temperature of the air in the tank also remains on 25°C. The process continues until the pressure in the tank reaches 1000kPa. Calculate the power required by the compressor. All processes are reversible. Solution An entropy and energy balance over the compressor alone cannot be used to solve the problem as the value of entropy of the air at the outlet of the compressor is not constant, it changes as the outlet pressure of the compressor rises. Consider the whole system. (It is left to the reader to draw a picture.) An energy balance gives: m₁u₁ + mihi + Win = m₂u2 + Qtot Where Qtot is the heat released by the compressor and the tank. We can determine m₁ and m₂ from the Ideal Gas Law and m; from a mass balance. We can read the values for enthalpy and internal energy from the tables, but it still leaves two unknowns, the work and heat transfer. However, as the process is reversible, the total entropy remains constant and the entropy at the beginning plus entropy in = entropy at the end plus entropy out: m181 + mįsi = m282 + Qtot Tair The total amount of heat released can now be calculated: Qtot = 298.15(2.337 × 6.863 +21.04 × 6.863 - 23.37 x 6.202) = 4606kJ The energy balance can now be used to calculate the work required by the compressor: 2805kJ.
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