Brayton cycle
This picture is the ideal cycle for a gas turbine:
and a representation of the closed cycle.
The hair blower dryer would use only the compressor and the heat input.
1-2 is an isentropic compression (constant entropy), where the air is compressed to a higher pressure and higher temperature.
2-3 is a constant pressure heat addition, with a rise in remperature.
for 1-2,compression, h = enthalpy, rate flow
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- W(in) = h(out)-h(in)
or,
-W(in) = Cp( Tout-Tin ) = Cp( T2 - T1 )
for 2-3, heat addition
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Qin = h(out) - h(in)
or
Q(in) = Cp( Tout - Tin ) = Cp( T3 - T2 )
We do not have a turbine, nor a heat rejection reservoir( heat is rejected to ambient) so both of these processes can be neglected.
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What is usually neglected in the ideal Brayton cycle is other forms of energy input and transfers such as potential, kinetic, chemical.
For a container control volume, with air moving in(state 1) and out(state 2) and having heat or work added to it,
From the first Law,
dE = ∂Q -∂W
and do not neglect the change in kinetic energy of the fluid due to its velocity,
we end up with,
q_{1-2} - W_{1-2} = u_{2} - u_{1} + ΔKE
If we separate the flow work from shaft work,
( ie flow work is PV of the fluid and we have it at the entrance and the exit )
q_{1-2} - W_{shaft,1-2} = h_{2} - h_{1} + ΔKE
or,
q_{1-2} - W_{shaft,1-2} = C_{p}( T_{2} - T_{2} ) + ΔKE
Obviously shaft work = 0 for the heating container.
The change in kinetic energy of the gas,
ΔKE = c_{2} ^{2}/2 - c_{1} ^{2}/2
If anyone wishes to find out the mass flow rate for an hair dryer and plug in some numbers...