What is meant by no gas enters or leaves the cylinder ?

[hahaha158]

What is meant by "no gas enters or leaves the cylinder"?

I have the following question.

A platform is supported on a piston by compressed air in a cylinder.
The mass of the platform and equipment being lifted is 1100kg. The pressure needed to
support this mass is 800kPa, and it rests initially at a height of 0.5m. The pressure supply
is closed so that no gas enters or leaves the cylinder. One of the pieces of equipment with a mass of 50kg is moved o the platform. The entire system is at room temperature (300K)

I am confused with the significance of the bolded line. I'm not sure whether it's implying constant volume, constant pressure, temperature, etc. Can someone explain this?

 

[Ned Stark]

I have the following question.

A platform is supported on a piston by compressed air in a cylinder.
The mass of the platform and equipment being lifted is 1100kg. The pressure needed to
support this mass is 800kPa, and it rests initially at a height of 0.5m. The pressure supply
is closed so that no gas enters or leaves the cylinder. One of the pieces of equipment with a mass of 50kg is moved o the platform. The entire system is at room temperature (300K)

I am confused with the significance of the bolded line. I'm not sure whether it's implying constant volume, constant pressure, temperature, etc. Can someone explain this?

P*V=n*R*T

from question; P don't change, and there is a finite amount of gas in chamber (i.e. n don't change)

so P don't change, n don't change (and R is a const. so it don't change), then what else could change (hint. if T change, then V change)

 

[hahaha158]

P*V=n*R*T

from question; P don't change, and there is a finite amount of gas in chamber (i.e. n don't change)

so P don't change, n don't change (and R is a const. so it don't change), then what else could change (hint. if T change, then V change)

Would the area change in this case? Because I need the area to find the volume, and according to my calculations it seems like it should, but it also seems a bit weird for the area of a platform to change

 

[ehild]

Would the area change in this case? Because I need the area to find the volume, and according to my calculations it seems like it should, but it also seems a bit weird for the area of a platform to change

No, the area of the piston does not change. But the piston can move up or down. Some weight is removed from the platform: that means the external force decreases. To get into equilibrium at the same temperature (300 K) what parameter of the gas has to change?
Initially the internal and external forces acting on the piston are in equilibrium: The weight of the 1100 kg load is balanced by he force the gas exerts when its pressure is 800 kPa. So what is the area of the piston?

ehild

 

[hahaha158]

No the area of the piston does not change. But the piston can move up or down.

ehild

sorry the question is

what is the new position of the platform?

so i was referring to the area of the platform, not the piston.

 

[ehild]

The platform is supported on the piston. What does it mean?

ehild

 

[hahaha158]

The platform is supported on the piston. What does it mean?

ehild

If the area is unchanging can we simplify the equation PV=nRT become

h=T since everything else is a constant or unchanging?

How would this relate to the mass though?

edit:i meant h=t when comparting the two heights so for this case

0.5m/300K = height2/T2?

 

[ehild]

The temperature does not change. The pressure does.

ehild

 

[hahaha158]

The temperature does not change. The pressure does.

ehild

Oh so according to the equation PV = nRT the only variables that change are P and V (since h changes)?

I'm a bit confused because I thought the above poster told me that pressure remains constant.

 

[ehild]

Oh so according to the equation PV = nRT the only variables that change are P and V (since h changes)?

Yes.

I'm a bit confused because I thought the above poster told me that pressure remains constant.

He was mistaken.

Think. What does it mean that some of the load is removed?

ehild

 

[hahaha158]

Yes.He was mistaken.

Think. What does it mean that some of the load is removed?

ehild

If the load is removed then the height will increase.

So iare there any errors in the following solution?

find area using Pi=m_ig/A
A*h=Vi

find Pf using Pf = m_fg/A

PiVi = PfA*h to solve for the unknown height?

thanks.

 

[ehild]

It is correct if the whole thing is in vacuum. Otherwise the 800 kPa is the gauge pressure, and the absolute pressure of the gas is 800 kPa +atmospheric pressure. As it was not mentioned, I think your solution is correct. ehild

 

[hahaha158]

It is correct if the whole thing is in vacuum. Otherwise the 800 kPa is the gauge pressure, and the absolute pressure of the gas is 800 kPa +atmospheric pressure. As it was not mentioned, I think your solution is correct.


ehild

ok thanks a lot for the help

 

[ehild]

You are welcome.

ehild

 

[hahaha158]

You are welcome.

ehild

sorry.

just one last question

the question asks for the maximum velocity

according to W=PdV
W should remain constant

and then using W=.5mv^2

wouldn't that mean you use m_f since m is inversely proportional to v and m is smalest at m_f?

 

[ehild]

Write the original question, please.

ehild

 

[hahaha158]

Write the original question, please.

ehild

A platform is supported on a piston by compressed air in a cylinder.
The mass of the platform and equipment being lifted is 1100kg. The pressure needed to
support this mass is 800kPa, and it rests initially at a height of 0.5m. The pressure supply
is closed so that no gas enters or leaves the cylinder. One of the pieces of equipment with a mass of 50kg is moved o the platform. The entire system is at room temperature (300K)

A)what is the height of the platform after the weight is removed?
B)what is the maximum velocity?

 

[ehild]

The gas exerts force and does work on the platform. That work increases both the potential and kinetic energy. The kinetic energy is maximum at the equilibrium height you calculated before, when the resultant force on the platform is zero, that is, the acceleration is zero. The platform will rise above the equilibrium height till the velocity becomes zero; after that, it moves backwards (ignoring friction).

ehild