Ideal gas piston in a cylinder question

[hahaha158]

Homework Statement

A chemical reaction vessel has a piston/cylinder arrangement, shown in gure 1 above.
When the reaction is complete, the gaseous products are at 250 KPa and 300C and can
be considered an ideal gas. The 50 kg piston has a diameter of 0.1 m and initially pushes
against a set of stops such that the height of the column of gas is 0.9 m limiting the volume.
The surrounding atmosphere is at 100 kPa and 20C. The cylinder now cools as heat is
transferred to the ambient surroundings.

(b) At what pressure does the piston begin to move down? What is the temperature of the
gas at this point?

Homework Equations

PV=nRT
Fg=mg
P=F/A

The Attempt at a Solution

I was thinking that to find the amount of pressure for the piston to move i could just find Fg=(9.8)(50)=490. Multiply that by the area of the piston and that would give the pressure to hold up the piston which would be around 62.4KPa. I then equated that with the given values of Pi=250000 Pa and Ti=573.15 K and solved for T which came out to be 143.12 K. Looking at the answer I don't think it is right because the T is not between the initial temperature of the gas or the surroundings, so I don't think that the gas can cool past the surrounding temperature. What am i doing wrong? Thanks

 

[Chestermiller]

Homework Statement

A chemical reaction vessel has a piston/cylinder arrangement, shown in gure 1 above.
When the reaction is complete, the gaseous products are at 250 KPa and 300C and can
be considered an ideal gas. The 50 kg piston has a diameter of 0.1 m and initially pushes
against a set of stops such that the height of the column of gas is 0.9 m limiting the volume.
The surrounding atmosphere is at 100 kPa and 20C. The cylinder now cools as heat is
transferred to the ambient surroundings.

(b) At what pressure does the piston begin to move down? What is the temperature of the
gas at this point?

Homework Equations

PV=nRT
Fg=mg
P=F/A

The Attempt at a Solution

I was thinking that to find the amount of pressure for the piston to move i could just find Fg=(9.8)(50)=490. Multiply that by the area of the piston and that would give the pressure to hold up the piston which would be around 62.4KPa. I then equated that with the given values of Pi=250000 Pa and Ti=573.15 K and solved for T which came out to be 143.12 K. Looking at the answer I don't think it is right because the T is not between the initial temperature of the gas or the surroundings, so I don't think that the gas can cool past the surrounding temperature. What am i doing wrong?


Thanks

Lets first focus on the gas in the cylinder. The gas is cooling at constant volume (right?) and constant number of moles. So can you predict using the ideal gas law how the pressure in the cylinder varies with the temperature in the cylinder as the gas cools?

Let's look at the piston as a free body. What is the force of gravity acting on the piston (you already calculated that)? What is the force of the outside atmosphere on the piston? What other forces are acting on the piston? Is the piston at static equilibrium before it loses contact with the stops? What happens once the pressure in the cylinder drops below the critical value at which the piston starts moving?