A rigid tank is filled with air. Initially, the tank has a pressure of 200 kPa,

Question

A rigid tank is filled with air. Initially, the tank has a pressure of 200 kPa, a temperature 27 degree C and a volume 10 m^3. Inside the tank, an electric resistor is operated with 220 V and 5 A for a period 30 minutes. Calculate the final temperature inside the tank. Large wind turbines with blade span diameters of over 100 m are available for electric generation. Consider a wind turbine with a blade span diameter of 100 m installed subjected to steady winds at 8 m/s. Taking the overall efficiency of the wind 1.25 kg/m^3, determine the electric power

Explanation / Answer

QUestion 2

Voltage = 220 V

Current = 5A

time = 30 minutes

Power Generated = VIt   = 220* 5 * 30 * 60 = 1980000 Joules

Here Pressure of Tank = 220 kPa

Temperature = 27 o C = 300 K

Volume = 10m3

Here work done dW = 0

so dU = dQ

Here dQ = 1980000 Joules = dU

dU = mCp dT

where CP = 1000 J/kg.K at 300K

so moles of the air in container n = PV/RT = 200 * 1000 * 10/ (8.314 * 300) = 801.86 moles

Mass of the air = MOleculer weight of air * number of moles = 29 g/mol * 801.86 = 23.254 Kg

so by putting values

1980000 Joules = 23.254 * 1000 * dT

dT = 85.15 0 C

so temperature will become 385.15 K = 112.15 0 C after 30 minutes.

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