Thermodynamics question - does power required mean same as power output?

[visharad]

How to find power required for adiabatic compressor?
Problem - Air enters an adiabatic compressor at 20 C and 1bar. The volumetric flow rate of air is 1 m3/s and it exits at 200 C. Determine the power required if the isentropic efficiency of the compressor is 80%.

Density of water = 1000 kg/m^3
Mass flow rate m = 1 m^3/s * 1000 kg/m^3 = 1000 kg/s
I know that power output is calculated by
m Cp (T2 - T1)

But what is meant by power required? Is it same as power output or is it power input?
If it is power output, then we can calculate it using m Cp (T2 - T1)
If it is power input, then can we use work required = power output/(isentropic efficiency) ?

The problem involves a range of temperatures. I have to use the values of density, Cp and any other constants needed at what temperature? Initial? Final? Average?

 

[NewtonianAlch]

I guess it means the power required to allow that 80% efficiency therefore it would be an input, if something is requiring power, it's awaiting an input.

 

[Andrew Mason]

How to find power required for adiabatic compressor?
Problem - Air enters an adiabatic compressor at 20 C and 1bar. The volumetric flow rate of air is 1 m3/s and it exits at 200 C. Determine the power required if the isentropic efficiency of the compressor is 80%.

Density of water = 1000 kg/m^3
Mass flow rate m = 1 m^3/s * 1000 kg/m^3 = 1000 kg/s
I know that power output is calculated by
m Cp (T2 - T1)

But what is meant by power required? Is it same as power output or is it power input?
If it is power output, then we can calculate it using m Cp (T2 - T1)
If it is power input, then can we use work required = power output/(isentropic efficiency) ?

The problem involves a range of temperatures. I have to use the values of density, Cp and any other constants needed at what temperature? Initial? Final? Average?

First find the power required to compress 1 m^3 of air every second. Hint: you have to determine the final compressed volume of that 1 m^3 of air. You are given its final temperature. What is the relationship between temperature and volume during an adiabatic compression? What is the work done?

Second, determine how much input power is required at 80% efficiency (ie only 80% of the input energy does work in compressing the air.

AM

 

[SteamKing]

Hint: The density of water (1000 kg/m^3) is not the same as the density of the air moving through the compressor.)

 

[rwisz]

Power required and power output are two different concepts in thermodynamics. Power required refers to the amount of power needed to operate a system, while power output refers to the amount of power that is actually produced by the system.

In the context of an adiabatic compressor, power required would refer to the amount of power needed to drive the compressor and compress the air. This would include the power needed to overcome any frictional losses and work done on the air to compress it.

To find the power required for an adiabatic compressor, we can use the equation P = m*Cp*(T2-T1), where P is the power required, m is the mass flow rate, Cp is the specific heat capacity, and T2-T1 is the change in temperature of the air. In this problem, we are given the values for m, Cp, and T2-T1, so we can calculate the power required using this equation.

If we want to take into account the efficiency of the compressor, we can use the equation P = Pout/η, where Pout is the power output and η is the isentropic efficiency. In this case, the power output would be equal to m*Cp*(T2-T1), so we can substitute this into the equation to get P = (m*Cp*(T2-T1))/η.

As for the values of density and Cp, we can use the values at any temperature as long as they are consistent throughout the calculation. In this case, since the problem does not specify a specific temperature, we can use the values at the initial temperature of 20°C or the final temperature of 200°C. Both values should give us the same result for power required.