A piston-cylinder machine contains 1 kg of air, initially at v = 0.8 m3/kg and 290 K. The gas is
compressed in a slow frictionless process to a specific volume of v = 0.2 m3/kg and a temperature of
580 K, according to the equation pv1.5 = 0.75 (where p is in bar and v as shown). Determine the work
and the heat transfer.

i assumed it was isothermal due to a slow process but apparently it is adiabtic due to the relationship p^v1.5 = 0.75. If its ever pressure times volume to a power is a consatnt is that always going to be an adaiabtic relationnship.
Original post by charliejoshua

A piston-cylinder machine contains 1 kg of air, initially at v = 0.8 m3/kg and 290 K. The gas is
compressed in a slow frictionless process to a specific volume of v = 0.2 m3/kg and a temperature of
580 K, according to the equation pv1.5 = 0.75 (where p is in bar and v as shown). Determine the work
and the heat transfer.

i assumed it was isothermal due to a slow process but apparently it is adiabtic due to the relationship p^v1.5 = 0.75. If its ever pressure times volume to a power is a consatnt is that always going to be an adaiabtic relationnship.

It is NOT isothermal as there is a change in temperature which should be obvious.

I think you need to use 1st law of thermodynamics to show that there is no heat transfer before concluding that it is adiabatic.
Original post by Eimmanuel
It is NOT isothermal as there is a change in temperature which should be obvious.

I think you need to use 1st law of thermodynamics to show that there is no heat transfer before concluding that it is adiabatic.