How can pressure and volume affect the work, energy, and heat of helium gas?

[pentazoid]

Homework Statement

Imagine some helium in a cylinder with initial volume of 1 liter and an initial pressure of 1 atm. Somehow the helium is made to expand to a final volume of 3 liters, in such a way that its pressure rises in diect proportion to its volume.

a) calculate the work done on the gas during this process , assuming that there are no "other" types of work being done.

b) Calculate the change in the helium's energy content during this process

c) calculate the amount of heat added to or removed from the helium during this process

d) Describe what you might do to cause the pressure o rise as the helium expands

Homework Equations

W=-integral(from V_i to V_f) P(V) dV (quasistatic)

W=-P*delta(V)

delta(U)= W+Q

delta(U)=f/2*NkT

The Attempt at a Solution

a) P=m*V+ b , where m is the slope and b is the y-int.

m=delta(P)/delta(V)= (3-1)/((3-1)=1 and b=0

P=V

W=integral (from 1 atm to 3 atm) (V dV)


b) delta(U)=f/2*NkT=(f/2)*PV

c)delta(U)=Q+W==> Q=delta(U)-W

d) some source of external heat such as a flame is probably causing the balloon to expand

Did I do everything correctly?

 

[chrisk]

P is directly proportional to V so

P = kV

where k is a constant.

Use this value for P in the work equation and integrate.

 

[pentazoid]

P is directly proportional to V so

P = kV

where k is a constant.

Use this value for P in the work equation and integrate.

Are my remaining solutions to the rest of my problems correct?

 

[pentazoid]

Are my remaining solutions to the rest of my problems correct?

I thought k would just equal 1 since when you find the equation for P, P=V

 

[chrisk]

The value k is a proportionality constant. One must know initial and final values of V and P to determine k. Since this was not given, the value k is unknown. Your answers will be in terms of k.

 

[pentazoid]

The value k is a proportionality constant. One must know initial and final values of V and P to determine k. Since this was not given, the value k is unknown. Your answers will be in terms of k.

but the initial and final values of P and V were given in the problem. here is a quote from the question. :"Some how the helium is made to expand to a final volume of 3 liters , in such a way that its pressure rises in direct proportion to its volume". So if my volume rises to 3 liters, then my pressure should rise to 3 atm.

 

[chrisk]

Please indicate what the final pressure is according to problem. There is no final pressure stated from what is given, only that the pressure varies directly with the volume.

 

[pentazoid]

Please indicate what the final pressure is according to problem. There is no final pressure stated from what is given, only that the pressure varies directly with the volume.

The problem doesn't state what the final pressure is. It just says that pressure varies in direct proportion to its volume. The problem says that there is an initial volume of 1 liter and an initial pressure of 1 atm. Since the pressure rises in direct proportion with its volume, if the final volume is 3 liters, doesn 't that mean the final pressure is 3 atm.

 

[chrisk]

No, it does not imply the final pressure is 3 atm. So, use k instead. Recall, k is the slope of the line in this case and two points are required to determine the slope of a line; you do not have the P coordinate of the second point.