A rigid tank contains an ideal gas at 300 kPa and 600 K. Half of the gas is withdrawn from the lank and the gas is at 100 kPa at the end of the process. Determine (a) the final temperature of the gas and (b) the final pressure if no mass were withdrawn from the tank and the same final temperature were reached at the end of the process.

Part (a)

Step 1:

A rigid tank contains an ideal gas at initial pressure and half of the gas is withdrawn from the lank and the gas at the end of the process.

Initial pressure of the ideal gas P1 = 300 kPa

Initial temperature of the gas T1 = 600 K

Final pressure after withdrawing half of the gas P2 = 100 kPa

Step 2:

From ideal gas equation

PV = mRT ----(1)

Where

P - Pressure

V - volume

m - total mass of the gas

R - gas constant

T - temperature

Step 3:

To find the final temperature of the gas. The pressure is reduced by withdrawing half of the gas. Assume that the volume remains the same. Therefore from the ideal gas equation

P1V = m1RT1 -----(2)

P2V = m2RT2 -----(3)

Since the gas is reduced to half of its previous value

m2 = -----(4)

Step 4:

Inserting (4) in (3) and dividing (2)

=

=

Step 5:

Rearranging the above equation for T2

T2 =

Therefore

T2 =

T2 = 400 K

The final temperature of the tank after reducing the gas is 400 K

Part (b)

Step 1:

Initial pressure of the ideal gas P1 = 300 kPa

Initial temperature of the gas T1 = 600 K

Final pressure of the gas P2 = 100 kPa

Step 2:

To find the final temperature if no mass is taken out. Therefore mass and volume remain constant. And from ideal gas equation

=