Question

One kg of air contained in a piston-cylinder assembly undergoes a process from an initial state whereT1=300K,v1=0.8m3/kg, to a final state whereT2=420K,v2=0.2m3/kg. Can this process occur adiabatically? If yes, determine the work, in kJ, for an adiabatic process between these states. If not, determine the direction of the heat transfer. Assume the ideal gas model withcv=0.72kJ/kg·Kfor the air.

Answer 1

Answer:

1. Yes, it can occur adiabatically.

2. The work required is: 86.4kJ

Explanation:

1. The internal energy of a gas is just function of its temperature, and the temperature changes between the states, so, the internal energy must change, but how could it be possible without heat transfer? This process may occur adiabatically due to the energy balance:

$U_{2}-U_{1}=W$

This balance tell us that the internal energy changes may occur due to work that, in this case, si done over the system.

2. An internal energy change of a gas may be calculated as:

$du=C_{v}dT$

Assuming $C_{v}$ constant,

$U_{2}-U_{1}=W=m*C_{v}(T_{2}-T_{1})$

$W=0.72*1*(420-300)=86.4kJ$