Question

A piston-cylinder device contains 0.18 kg of air initially at 2 MPa and 350°C. The air is first expanded isothermally to 500 kPa then compressed polytropically with a polytropic exponent of 1.2 to the initial pressure, and finally compressed at the constant pressure to the initial state. Determine the boundary work for each process and the net work of the cycle. The properties of air are R=0.287 kJ/kg K and k=14.

The boundary work for the isothermal expansion process is ___kJ

Answer 1

The boundary work for the isothermal expansion process, when air is expanded isothermally from 2 MPa to 500 kPa, can be determined using the isothermal work formula, resulting in work done of 77.53 kJ.

Step-by-step explanation:

To determine the boundary work for the isothermal expansion of air in a piston-cylinder device, we can use the formula for work done by an ideal gas during an isothermal process: W = nRT "ln(P1/P2). Since we are given the mass of the air (0.18 kg), the initial pressure (2 MPa), and the final pressure (500 kPa), we can convert the pressures to the same units (Pascals) and use the gas constant for air (R = 0.287 kJ/kg·K).

The temperature given is in Celsius but for thermodynamic calculations it needs to be converted into Kelvin. The conversion formula is T(K) = T(°C) + 273.15. Thus, the temperature in Kelvin is T = 350 + 273.15 = 623.15 K.

The number of moles (n) can be calculated using the equation n = m/M, where m is mass and M is the molar mass of air, approximately 28.97 g/mol. However, since R here is given in terms of mass rather than moles, we can directly use the mass in the work equation without needing to convert to moles, simplifying the calculation.

Substituting the values into the isothermal work formula, we get the boundary work for the isothermal expansion process as W = (0.18 kg)(0.287 kJ/kg·K)(623.15 K)"ln(2000000/500000) = 77.53 kJ.