What is the Work Done on an Ideal Gas Under Isothermal Compression?

In summary, the problem involves an ideal gas compressed reversibly against a piston, with its temperature changing in such a way that the relationship P=AV is satisfied at each instant. The question asks for the work done on the gas in terms of n, R, and T1. Using the work equation for an isothermal process, it can be evaluated by integrating AV dV from V1 to V2, where V1 and V2 are constants. By expressing V2 in terms of V1 (using the given relationship) and V1 in terms of T1, the final answer of -3nRT1/8 is obtained.
  • #1
djaymilla
3
0
An ideal gas originally at a temperature T1 and pressure P1 is compressed recersibly against a poston to a volume equal one-half of its original volume. The temperature of the gas is caried during the compression so that at each instant the relatoion P=AV is satisfied, where A is constant. Find the word done on the gas in terms of n, R, and T1.


PV=nRT
P=AV
AV^2=RT
dW= -PdV
W= - (integral from V1 to V2) PdV


I have the answer: [-3nRT1/8] but I cannot figure out how it is derived. I have tried using the work equation for an isothermal equation as well: W=nRT (integral from V1 to V2) dV/V where W=nRT ln (V2/V1)
 
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  • #2
Hi djaymilla, welcome to PF. Why not just evaluate the work integral, plugging in AV for P?
 
  • #3
Hey Mapes, thanks for the welcome. I guess I am confused with this problem because I don't have concrete terms with which to integrate. I'm not sure how to carry out the integral...

(sorry, this may seem elementary, but I'm now going BACK to school, and have been out of the physics/calculus game for quite some time)
 
  • #4
You're almost there. You will need to integrate AV dV from V1 to V2, where A, V1, and V2 are constants. I'm sure you'll be able to figure this out. The remaining steps consist of expressing V2 in terms of V1 (you already described this relationship) and expressing V1 (more precisely, V1^2, hint hint) in terms of T1. Good luck.
 

1. What is the definition of thermodynamic work function?

Thermodynamic work function is a measure of the minimum energy required to remove an electron from a solid surface into vacuum. It is a key concept in thermodynamics and is used to understand and predict the behavior of materials under various conditions.

2. How is thermodynamic work function different from other work functions?

Thermodynamic work function is specific to the removal of electrons from a solid surface into vacuum, while other work functions, such as the photoelectric work function, are specific to the removal of electrons due to the absorption of photons. Additionally, thermodynamic work function takes into account the temperature and pressure of the system, while other work functions may not.

3. What factors affect the value of thermodynamic work function?

The value of thermodynamic work function is affected by the electronic structure and chemical composition of the material, as well as the temperature and pressure of the system. It can also be influenced by external factors such as electric fields and surface defects.

4. How is thermodynamic work function measured?

Thermodynamic work function is typically measured using various experimental techniques, such as Kelvin probe force microscopy, photoemission spectroscopy, and thermionic emission. These methods involve measuring the energy required to remove electrons from a solid surface and comparing it to a reference material.

5. What is the significance of thermodynamic work function in material science?

Thermodynamic work function is a fundamental property of materials that can provide important insights into their electronic properties and behavior. It is used in various applications, such as in the development of energy-efficient materials and in the study of surface reactions and catalysis.

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