How Much Heat is Needed to Raise a Piston in a Heated Ideal Gas Cylinder?

[Myr73]

An ideal gas is placed in a tall cylindrical jar of crosssectional area 0.080m^2. A frictionless 0.10kg movable piston weight is supported by the gas pressure in the jar. When the gas is heated (at constant pressure) from 25C to 55C , the piston rises 1.0cm. How much heat was required for this process? Assume atmospheric pressure outside.

A= 0.08m^2 , m=0.1kg, , Delta P= 0 --> Q= Delta U + W= Delta U + P(Delta V)
Tl= 298K , Th= 328K , d=0.01m , Q=?

I am unsure where to begin here.

 

[Chestermiller]

An ideal gas is placed in a tall cylindrical jar of crosssectional area 0.080m^2. A frictionless 0.10kg movable piston weight is supported by the gas pressure in the jar. When the gas is heated (at constant pressure) from 25C to 55C , the piston rises 1.0cm. How much heat was required for this process? Assume atmospheric pressure outside.

A= 0.08m^2 , m=0.1kg, , Delta P= 0 --> Q= Delta U + W= Delta U + P(Delta V)
Tl= 298K , Th= 328K , d=0.01m , Q=?

I am unsure where to begin here.

The amount of heat depends on the amount of gas in the jar. The greater the mass of gas, the greater the amount of heat required to raise its temperature 30C. What is the pressure of the gas in the jar? From the ideal gas law, how many moles of gas are there in the jar?

For a constant pressure process, how is the amount of heat added Q related to the change in enthalpy (ΔH) of the gas? For an ideal gas, what the equation for the change in enthalpy in terms of the temperature change and the heat capacity?

Chet

 

[Myr73]

ok, umm -- How many moles, U= 3/2nRT , Where R is 8.314 J/mol.K , T would be 298K??, And then there would be PV=nRT, But I don't know how to find P here without knowing U first.

Im not sure what enthalpy is ?, I have heard of entropy but not enthalpy, I don't think we cover that in this course-

 

[Chestermiller]

To get the pressure, you do a free body diagram on the piston, and include the weight of the piston and the air pressure from above. You have had freshman mechanics, correct?

Chet

 

[Chestermiller]

ok, umm -- But I don't know how to find P here without knowing U first.

That's very interesting. Please tell me about your methodology for finding P if you know U first.

Chet

 

[Myr73]

umm.. I think I was thinking if I had U then I would know n, and then I don't know- and I am unsure of the diagram,

 

[Chestermiller]

umm.. I think I was thinking if I had U then I would know n, and then I don't know- and I am unsure of the diagram,

When you had freshman physics, they taught you how to use free body diagrams to do force balances on objects. There was a reason that they taught you this methodology. It was so that you could use it in more advanced analyses (such as your present thermo problem). Draw an isolated diagram of the piston, and draw arrows in the diagram to show all the forces acting on the piston. What forces have you identified as acting on the piston (there are 3)? If you are unable to do this, please go back and review your freshman physics textbook and notes. You won't be able to do your present thermo problem until you can use the force balance on the piston to determine the gas pressure.

Chet

 

[Myr73]

umm ok, I will work on that and get back to you!

 

[Myr73]

Ok, I understand how to do a general diagram of it, I think it would be, force of gravity pushing down, Gas Pressure pushing up (witch balances it out) and then the Heat would push up further. And the gravitational force would be mg. But I still don't get how I would calculate the air pressure-

 

[Chestermiller]

Ok, I understand how to do a general diagram of it, I think it would be, force of gravity pushing down, Gas Pressure pushing up (witch balances it out) and then the Heat would push up further. And the gravitational force would be mg. But I still don't get how I would calculate the air pressure-

You're starting to get the idea. The gas pressure pushing up is equal to mg plus the air pressure pushing down. The heat doesn't push anything . And you don't have to calculate the air pressure . It is one atmosphere. Do you know what one atmosphere is in Pa?

Chet

 

[Myr73]

Oh I see, yes I do- thanks :)