Work in Adiabatic/ Isothermal and Piston

In summary, the conversation discusses determining the pressure change, heat released or absorbed, and work done on or by a gas in an adiabatic and isothermal process. The equations for work in both processes are derived and it is questioned how to show that work in isothermal is greater than in adiabatic. The possibility of using double integrals is also considered. It is suggested to compare the PV graphs for both processes to determine which one has a greater work.
  • #1
~Sam~
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Homework Statement



Is work greater in adiabatic or isothermal process?

A piston with oxygen has a final volume 1/4 the initial. The temperature is also 5 times greater. Determine pressure change, heat released or absorbed, and work done on or by gas.

Homework Equations



the work for adiabatic and isothermal. General w= -integral pdv, conservation of energy deltaV=Q+w

The Attempt at a Solution



I have derived the the expressions for work in both adiabatic and isotherm process from their integrals. ie:- Kln(vf/vi) and -k(vf1-gamma-vi1-gamma)/(1-gamma). But I'm not sure how to show that work in isothermal > adiabatic.

For the second part I'm just not sure how to take into account both temperature and pressure, and I can't assume that it's adiabatic/isothermal in the beginning. Any ideas?

Note: I did trying doing the double integral, dvdt...but i still only get an expression only.
 
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  • #2
Consider a gas undergoing an isothermal and an adiabatic change both having the same change in volume and both starting from the same point on a PV diagram.
Sketching the corresponding PV graphswill show which process has tha bigger work.
 

FAQ: Work in Adiabatic/ Isothermal and Piston

What is the difference between adiabatic and isothermal work?

Adiabatic work refers to work done on or by a system while there is no heat exchange with the surroundings. This means that the internal energy of the system remains constant. In contrast, isothermal work is work done on or by a system while its temperature remains constant. This results in no change in the internal energy of the system.

How does a piston affect work in adiabatic and isothermal processes?

A piston is a device used to contain a gas within a closed system. In adiabatic processes, the piston can compress or expand the gas, leading to work being done on or by the system. In isothermal processes, the piston helps maintain a constant temperature by allowing the gas to expand or contract as needed to maintain equilibrium.

What factors affect the amount of work done in adiabatic and isothermal processes?

The amount of work done in adiabatic and isothermal processes depends on the initial and final states of the system, as well as the pressure and volume of the gas. Additionally, the type of process (adiabatic or isothermal) and the presence of a piston can also affect the amount of work done.

How do adiabatic and isothermal work relate to the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted. In adiabatic processes, no heat is exchanged, so the change in internal energy of the system is equal to the work done on or by the system. In isothermal processes, the change in internal energy is equal to the heat added or removed from the system, plus the work done on or by the system.

What are some real-world examples of adiabatic and isothermal work?

An example of adiabatic work is the compression of air in a bicycle pump. As the air is compressed, work is done on the system, causing its temperature to increase. An example of isothermal work is the expansion of steam in a steam engine. The steam expands while maintaining a constant temperature, allowing it to do work on the piston and move the engine.

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