number 6 A compressor with an efficiency of 75% is used to pressurize an air tan

Question

number 6

A compressor with an efficiency of 75% is used to pressurize an air tank to 100 psi. The volume of the tank is 11 gallons and the temperature is 25 degree C (298 degree K). Assume air is an ideal gas so PV = nRT P in atm, V in liters, n in mol, T in degree K, R in (atm)/(mol* degree K) How much energy (joules) must be delivered to the compressor? Deliverable (with units): Given information (define variables) Equation Unit conversions needed: Solution: How many mols of air are in the tank at 100 psi? Deliverable (with units) Given information (define variables) equation Unit conversions needed: Solution: It takes 10 minutes to fill the tank to the pressure of 100 psi. What is the power input to the compressor in units of horsepower? Deliverable (with units): Given information (define variables) Equation Unit conversions needed: Solution:

Explanation / Answer

efficiency of compressor= out put energy ( work done by the compressor)/ input energy to the compressor

work done by the compressor = PV = (100 psi).(11 gallons)

100psi =689476 Pascals

11 gallons= 0.0416 cubic meter

work done by the compressor= 689476x0.0416 =28.68 KJ

efficiency =0.75

hence energy supplied = 28.68/0.75= 38.24KJ

energy = power x time

time= 10 minutes = 600 seconds

38.24KJ/600 = 63.73 watts =0.085 hP= 0.085 horse power

1 horse power = 746 watts

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