Determine the work and heat transfer

In summary: The process is polytropic, meaning that PVn = constant. Chetan has correctly found the equation for the work in terms of pressure and volume, and has also determined the value of n to be 1.14. However, he is unsure about the units and how to convert the work to BTU per lb. He is also unsure how to use the first law of thermodynamics to find the heat transfer. Chetan is seeking help and would appreciate any guidance.
  • #1
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Homework Statement



Steam in a piston-cylinder assembly undergoes a polytropic process. Kinetic and potential energy effects are negligible. For the process, determine the work and heat transfer, each in Btu per lb of steam.

p1 = 100 lbf/in2
p2 = 40 lbf/in2
v1 = 4.934 ft3/lb
v2 = 11.04 ft3/lb
u1 = 1136.2 Btu/lb
u2 = 1124.2 Btu/lb

Homework Equations



ΔE = Q - W

W = ∫v1v2pdV

The Attempt at a Solution



Since the process is polytropic, PVn = constant = p1V1n = p2V2n

Thus, W = ∫v1v2(constant/Vn)dV = (p2V2 - p1V1)/(1-n)

I used the relation p1V1n = p2V2n to find n, which gives me n = 1.14

Then, my plan is to plug the numbers into my integrated work function, but I am extremely confused on the units of this and I'm not really sure if I'm even working in the right direction. Basically I've gotten stuck at this point. Any help would be much appreciated.
 
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  • #2
Your equation for the work is correct. To get the work in BTU/lb, you need to first get it in ft-lbf/lb, and then convert the ft-lbf to BTU. Then you use the first law of thermo to get the heat, since you already know both W and ΔE.

Chet
 

FAQ: Determine the work and heat transfer

1. What is the definition of work in terms of thermodynamics?

In thermodynamics, work is defined as the energy transferred when a force is applied to an object and moves it a certain distance in the direction of the force. It is typically represented by the symbol W and is measured in joules (J).

2. How is work calculated in a thermodynamic system?

The work done in a thermodynamic system is calculated by multiplying the force applied to the object by the distance it moves in the direction of the force. Mathematically, it can be represented as W = F x d, where W is work, F is force, and d is distance.

3. What is the relationship between work and heat transfer?

Work and heat transfer are both forms of energy transfer. However, the main difference is that work involves the transfer of energy through mechanical means, while heat transfer involves the transfer of thermal energy. In some thermodynamic processes, both work and heat transfer may occur simultaneously.

4. How do you determine the sign of work and heat transfer in a thermodynamic process?

The sign of work and heat transfer is determined by the direction of energy transfer. If energy is being transferred to the system, the work and heat transfer will have a positive sign. If energy is being transferred from the system, the work and heat transfer will have a negative sign.

5. Can work and heat transfer be converted into each other?

Yes, work and heat transfer can be converted into each other through different thermodynamic processes. For example, in a heat engine, heat is converted into work, while in a refrigerator, work is used to transfer heat from a cooler environment to a warmer one.

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