1) A dentist drill is driven by a small, high-speed turbine operating on compres

Question

1) A dentist drill is driven by a small, high-speed turbine operating on compressed air which produces a shaft power output of 150W . At the inlet to the turbine the air has a pressure of 450kPa and a temperature of 65oC . At the exit of the turbine, the air has a pressure of 150kPa and a temperature of -25oC. Both the inlet and exit velocities may be assumed to be negligable and the process to be adiabatic.

Assume a constant specific heat (at constant pressure) of air, Cpair = 1004 J/kg K

Note, sign convention requires work done by device to be positive

What is the required mass flow rate of air through the turbine to deliver the required power output ?

( ? ) grams/s

2) A kitchen refrigerator removes 2.5kJ of energy from the frozen food cabinet using 1kJ of work done by the electrically powered compressor.

a) How much energy is released into the kitchen ? ( ? ) kJ (Answer to 1dp)

b) What is the coefficient of performance of the refrigerator ? ( ? ) (Answer to 1dp)

Please Show Work

Explanation / Answer

Name "G" the required mass flow rate of air through the turbine. [mass/ sec]
L = work done by device / mass
P = power output

P = L * G
then
G = P/L

We haven't L but we know that the process may be assumed adiabatic (Q (heat) = 0)
So for the 1 ° principle of thermodinamic :
L +Q = ΔE
but Q = 0 so
L = ΔE
ΔE = h (enthalpy) + ΔEc (kinetic energy) + ecc...
ΔEc = 0 because the text says " Both the inlet and exit velocities may be assumed to be negligable"

so
L = h = cp * ΔT = 1004 J/kg K * (65- (-25) = 90360 J /kg
G = 150/ 90360 = 1.66 grams/s

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