One liter of an ideal monatomic gas (gamma=5/3) at atmospheric pressure (1.0 atm

Question

One liter of an ideal monatomic gas (gamma=5/3) at atmospheric pressure (1.0 atm) and a temperature of 300K is used in the following cycle: an adiabatic compression to one half its original volume, followed by a constant-volume cooling to 300K, followed by an isothermal expansion back to original volume.

Determine the work done by the gas, the heat entering the gas and the change in thermal energy of the gas in each leg of the cycle. Organize answer in table.

is this cycle allowed by the second law of thermodynamics? what kind of heat machine does this cycle represent? heat engine? refrigerator? explain

Explanation / Answer

Thus, the only part of the problem where work is done is when the pressure is held constant and the volume expands.

p => 1.0 atm x (101300 pascal) = 101300 pascal (pascal is metric units of N/m^2)

?V => 1L - 0.5 L = 0.5 L (1 m^3 / 1000 L) = 0.0005 m^3 (again, we use metric units)

W = p?V = 101300 N/m^2 (0.0005 m^3) = 506.5 N m = 506.5 J

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