Homework SourseAn ideal gas of volume 2 ft cubed is contained within a cont
An ideal gas of volume 2 ft cubed is contained within a container having an area of 1 ft squared and a volume of 5 ft cubed. The pressure of the gas is 10 atm, the force of the piston is 1440 lbf, and an external force is applied to keep the piston in place. The external pressure is 1 atm. When the external force is released, the piston rises without friction up the container. The gas in the container is always kept at the same temperature. What is the velocity of the moving piston?
Hint: for ideal gas. PV=nRT
PV=constant
An ideal gas of volume 2 ft cubed is contained within a container having an area of 1 ft squared and a volume of 5 ft cubed. The pressure of the gas is 10 atm, the force of the piston is 1440 lbf, and an external force is applied to keep the piston in place. The external pressure is 1 atm. When the external force is released, the piston rises without friction up the container. The gas in the container is always kept at the same temperature. What is the velocity of the moving piston?
Hint: for ideal gas. PV=nRT
PV=constant
Hint: for ideal gas. PV=nRT
PV=constant
Solution
As the temperature T is constant, it is a isothermal expansion. With Isothermal process work done
W = nRTln(V2/V1)
Initial volume = 2cft, final volume = 5 cft
W = nRTln(5/2)
With initial condition
10*14.696*144*2 = nRT ( 1 atm = 14.696 psi)
W = 10*14.696*2*ln(5/2)
= 38781.528
If v is the velocity of the piston and m is the mass then
mv2 /2 = 38781.528
mass of the piston = 1440/32.17 = 44.76 lbs
average velocity of the piston = sqrt(38781.53*2/44.76)
= 41.63 ft/s
