Question

A vertical piston-cylinder device initially contains 0.2 m3 of air at 20°C. The mass of the piston is such that it maintains a constant pressure of 300 kPa inside. Now a valve connected to the cylinder device is opened, and air is allowed to escape until the volume inside the cylinder is decreased by one-half. Heat transfer is allowed during the process so that the temperature of the air in the cylinder remains constant. Determine (a) the amount of air that has left the cylinder and (b) the amount of heat transfer.

Answer 1

Answer:

Amount of air left in the cylinder=m$_{2}$=0.357 Kg

The amount of heat transfer=Q=0

Explanation:

Given

Initial pressure=P1=300 KPa

Initial volume=V1=0.2$m^{3}$

Initial temperature=T$_{1}$=20 C

Final Volume=$V_{2}$=0.1 $m^{3}$

Using gas equation

$m_{1}=((P_{1}*V_{1})/(R*T_{1}))$

m1==(300*0.2)/(.287*293)

m1=0.714 Kg

Similarly

m2=(P2*V2)/R*T2

m2=(300*0.1)/(0.287*293)

m2=0.357 Kg

Now calculate mass of air left,where me is the mass of air left.

me=m2-m1

me=0.715-0.357

mass of air left=me=0.357 Kg

To find heat transfer we need to apply energy balance equation.

$Q=(m_{e}*h_{e})+(m_{2}*h_{2})-(m_{1}*h_{1})$

Where me=m1-m2

And as the temperature remains constant,hence the enthalpy also remains constant.

h1=h2=he=h

Q=(me-(m1-m2))*h

me=m1-me

Thus heat transfer=Q=0