Question
Download Solution PDFA mass of 2.4 kg of air at 150 kPa and 12°C is contained in a gas - tight, frictionless piston - cylinder device. The air is then compressed to a final pressure of 600 kPa. During this process, heat is transferred from the air in such a way that the temperature inside the cylinder remains constant. Calculate the work input during the process.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
During isothermal compression, temperature remains constant and the work done by the gas is given by
\(dW = {P_1}{V_1}\ln \frac{{{V_2}}}{{{V_1}}} = {P_1}{V_1}\ln \frac{{{P_1}}}{{{P_2}}}\) = \(mRT_1 \ln \frac{{{P_1}}}{{{P_2}}}\)
Calculation:
Given:
P1 = 150 kPa, T = 12°C = 285 K, P2 = 600 kPa, m = 2.4 kg, R = 0.287 kJ/Kg-K
The work done by the gas is
W = \(mRT_1 \ln \frac{{{P_1}}}{{{P_2}}}\) = \( 2.4 \times {0.287} \times 285~\times\ln \frac{{150}}{{600}} = -272.14\;kJ\;\)
Last updated on May 28, 2025
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