Thermodynamic process, gas expansion

In summary, the problem involves finding the final pressure of 1kg of air at 398K that expands until its volume is 5 times its initial value. The process is not isochoric, isobaric, or adiabatic, leaving it as isothermic. However, the calculation of work is unknown and the only progress that can be made is through dU = (3/4)dW. It may be possible to express internal energy in terms of n and T or P and V, but the equation for dU may need to be revised. Additionally, the air is diatomic.
  • #1
usn7564
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Homework Statement


1kg air with the pressure 10^6 Pa and temperature 398K expands until the volume is 5 times its' initial value. The expansion occurs so that in every moment the absorbed heat energy (dQ) is 1/4 of the work done by the gas. Find the final pressure. 1kmol of air has the mass 29kg, [tex]C_v=\frac{5}{2}R[/tex]

The attempt at a solution
Made numerous but it eventually stopped being about physics ended up being a desperate plug and chug. More interested in learning where I'm going wrong with my general line of thought.

I'm ruling out that the process is isochoric or isobaric, the former by definition and the latter because the book barely has any trick questions and I also looked at the answer.
And it's not adiabatic because dQ=/=0. That leaves isothermic but as [tex]dQ = C_v \nu dT[/tex] it can't be isothermic either.
And if it's none of those I simply don't know how to calculate the work, and as the work depends on path I can hardly chose an arbitrary one.

The only step forward I can take is [tex]dU=\frac{3}{4}dW[/tex], as dQ = 1/4 dW. I thought of somehow calculating change in internal energy as it doesn't depend on path, but it does depend on temperature and I don't have dT (nor do I know how to get it).

Any input would be appreciated, thanks.
 
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  • #2
Air is diatomic. Can you use that to express U in terms of n and T (or better, express U in terms of P and V)? Also, I'm not sure about your sign for dU = (3/4)dW. Is dW the work done by the gas or the work done on the gas?
 

1. What is a thermodynamic process?

A thermodynamic process is a physical phenomenon that involves the transfer of energy between a system and its surroundings. It is described by thermodynamic principles and laws, and can be classified as either reversible or irreversible.

2. How is gas expansion related to thermodynamic processes?

Gas expansion is a type of thermodynamic process where a gas expands and does work on its surroundings, typically by pushing against a piston. This process can be either adiabatic (no heat exchange) or isothermal (constant temperature).

3. What is the first law of thermodynamics and how does it apply to gas expansion?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. In the case of gas expansion, the work done by the gas on its surroundings is equal to the change in internal energy of the gas plus the heat absorbed or released.

4. How does gas expansion affect the temperature and pressure of the gas?

During gas expansion, the temperature of the gas will decrease if the process is adiabatic, or remain constant if the process is isothermal. This is due to the decrease in internal energy of the gas as it does work on its surroundings. The pressure of the gas will also decrease as it expands and does work.

5. What factors can affect the efficiency of a gas expansion process?

The efficiency of a gas expansion process can be affected by factors such as the type of gas, the initial and final volumes and temperatures, and the rate at which the expansion occurs. It can also be influenced by external factors such as friction and heat loss to the surroundings.

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