A mass of 1.3 kg of air at 120 kPa and 24°C is contained in a gas-tight, frictionless piston-cylinder device. The air is now compressed to a final pressure of 600 kPa. During the process, heat is transferred from the air such that the temperature inside the cylinder remains constant. Calculate the magnitude of work input during this process.

Question

Emerson Henderson

Engineering

3 September, 07:26

A mass of 1.3 kg of air at 120 kPa and 24°C is contained in a gas-tight, frictionless piston-cylinder device. The air is now compressed to a final pressure of 600 kPa. During the process, heat is transferred from the air such that the temperature inside the cylinder remains constant. Calculate the magnitude of work input during this process.

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Emma Yates · Answer 1

The magnitude of work input is 178.79 kJ

Explanation:

The process is an isothermal compression process because the temperature inside the cylinder is constant.

W = nRT ln (P1/P2)

n is the number of moles of air in the cylinder = mass/MW = 1.3/29 = 0.045 kgmol

R is gas constant = 8.314 kJ/kgmol. K

T is temperature of air = 24 °C = 24+273 = 297 K

P1 is intial pressure of air = 120 kPa

P2 is final pressure of air = 600 kPa

W = 0.045*8.314*297 ln (120/600) = 111.11661 ln 0.2 = 111.11661 * - 1.609 = - 178.79 kJ