Thermodynamic Work Relations

In summary, the equations for calculating the work done on an ideal gas during different processes such as isometric, isothermal, polytropic, and isobaric were discussed. The most general equation for a polytropic process is PV^n = constant, and for an isentropic compression, n is the ratio of specific heats. For an isobaric process, n = 0, and for an isothermal process, n = 1. The integration of these equations yields the work done on the gas. A helpful resource for further information is the website http://webbook.nist.gov/chemistry/.
  • #1
blinder
4
0
I was wondering if anyone knows where i can find the work relations for an ideal gas including isometric, isothermal, polytropic, isobaric, etc.
 
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  • #2
Hi blinder. I'm assuming you're looking for the equations to calculate the work done on an ideal gas when undergoing the various processes you've listed. A polytropic process is the most general, so we can start with that. Also, the equations should work just as well for compression or expansion (work in or out of the gas).

As you must already know PV^n = constant is a polytropic process. If you compress a gas, the work done is the integral of PdV. If we integrate that for a polytropic process you end up with:

W = (m R (T2 - T1) / (1-n) = (P2 V2 - P1 V1) / (1-n)
where m = mass
R = Gas Constant
T = temperature
n = polytropic exponent
P = absolute pressure
V = total volume
(for any value of n except 1)

For an isentropic compression, n = the ratio of specific heats of the gas (ex: 1.667 for a monotomic gas, 1.4 for a diatomic gas, etc...)

For an isobaric process, n = 0

For an isothermal process, n = 1 so you need to do the integration using n=1 which comes out to:

W = mRT ln (V2/V1) = mRT ln (P1/P2)

Hope that helps.
 
  • #3

1. What is the definition of thermodynamic work?

Thermodynamic work is the transfer of energy from one system to another through mechanical means, such as force applied over a distance.

2. How is work related to heat in thermodynamics?

In thermodynamics, work and heat are both forms of energy transfer. Heat is the transfer of energy due to a temperature difference, while work is the transfer of energy due to a force acting over a distance.

3. What are the different types of thermodynamic work?

The three types of thermodynamic work are mechanical work, electrical work, and surface work. Mechanical work involves the movement of an object, electrical work involves the movement of charged particles, and surface work involves the change in surface area of a system.

4. What is the first law of thermodynamics and how does it relate to work?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. This law relates to work in that work is a means of transferring energy from one system to another.

5. How is work calculated in thermodynamics?

The formula for calculating work in thermodynamics is W = F x d, where W is work, F is the force applied, and d is the distance over which the force is applied. This formula applies to all three types of thermodynamic work.

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