A closed system containing a gas is to undergo a reversible process

In summary, we used the first law of thermodynamics and the ideal gas law to solve for the work done per unit mass in a reversible process for a closed system containing a gas. The final answer is -18.7 Btu/lbm.
  • #1
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Homework Statement


A closed system containing a gas is to undergo a reversible process from an intial specific volume of 2 ft^3/lbm and a intial pressure of 100 psia. The final pressure is 500 psia. Compute the work done per unit mass.

a. Pv= constant
b. pv^-2 = constant

Homework Equations


(1) p2/p1 = (v1/v2)^k

w = ∫Pdv

The Attempt at a Solution



Using equation (1) I solved for v2, w = ∫Pdv, but p is not constant, so i don't know how to find the work. Maybe step one is wrong, but I have the final answer = -59.6 Btu/lbm

Thanks!
 
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  • #2


Hi there,

To solve this problem, we can use the first law of thermodynamics for a closed system, which states that the change in internal energy of the system is equal to the heat added to the system minus the work done by the system. In this case, we are only interested in the work done, so we can ignore the heat term.

From the ideal gas law, we know that for a reversible process, PV = constant. Therefore, we can use this relation to solve for the final specific volume, v2, in terms of the initial specific volume, v1, and the initial and final pressures, p1 and p2:

p1v1 = p2v2
v2 = (p1/p2)v1

Now, we can use this expression for v2 in our work equation, w = ∫Pdv, to solve for the work done per unit mass:

w = ∫p1v1^2/(p1/p2)^2 dv
w = ∫(p1/p2)^2v1^2 dv
w = (p1/p2)^2v1^2 ∫dv
w = (p1/p2)^2v1^2 (v2 - v1)

Substituting in our expression for v2, we get:

w = (p1/p2)^2v1^2 [(p1/p2)v1 - v1]
w = (p1/p2)^3v1^3 - (p1/p2)^2v1^2

Finally, we can plug in the given values for p1, p2, and v1 to solve for the work done per unit mass:

w = (100/500)^3(2)^3 - (100/500)^2(2)^2
w = (-0.008) - (0.016)
w = -0.024 ft^3-lbf/lbm

Converting to Btu/lbm, we get:

w = (-0.024 ft^3-lbf/lbm)(778.169 ft-lbf/Btu)
w = -18.7 Btu/lbm

So, the final answer is actually -18.7 Btu/lbm, not -59.6 Btu/lbm as stated in the forum post.

I hope this helps! Let me know if you have any further questions.
 

1. What is a closed system?

A closed system is a type of thermodynamic system that does not allow the exchange of matter with its surroundings. This means that the system is isolated and does not interact with any external substances.

2. What does it mean for a process to be reversible?

A reversible process is one in which the system can be brought back to its original state by reversing the path of the process. This means that the system is in equilibrium at every stage of the process and there is no net energy or matter transfer.

3. How does a gas behave in a closed system?

In a closed system, a gas will expand or contract based on changes in temperature and pressure. If the gas is allowed to expand, it will do so until it reaches a new equilibrium state where the pressure and temperature are balanced.

4. What is the significance of a reversible process in a closed system containing a gas?

A reversible process in a closed system containing a gas allows for maximum efficiency and minimal energy loss. This is because the system is in equilibrium at every stage, meaning there is no net energy transfer and the process can be reversed without loss of energy.

5. Can a closed system containing a gas undergo an irreversible process?

Yes, a closed system containing a gas can undergo an irreversible process. In this case, the system will not be in equilibrium at every stage and there will be a net transfer of energy. This can result in a loss of efficiency and potential changes in the system's properties.

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