Work calculation for isothermal compression

In summary, the conversation discusses the equations for calculating work done by an ideal gas and in a constant-pressure process. The person attempted to solve a problem using these equations but encountered difficulties. They received clarification on the type of work being asked for and realized that the given data was not consistent with the ideal gas law.
  • #1
PNGeng
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Homework Statement


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Homework Equations


Work done by an ideal gas, isothermal process: W=n*R*T*ln(V_f / V_i)
Work, constant-pressure process: W=p*(V_f - V_i)

The Attempt at a Solution


I first tried plugging n=1, R=8.31, T=273.15, V_f=17.5 L, V_i=24 L into the first equation and it didn't work.

I then tried the constant-pressure formula with the corresponding values given from the problem (p=.937 atm, V_f=17.5 L, V_i=24 L) and it didn't work either.

This problem seems pretty straight forward but I can't get the right answer. Help?
 
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  • #2
The work formula you used is for the work of the gas. The problem asks the work of an external agent. Is the external work positive or negative?

The data given are not consistent with the ideal gas law. 1 mol oxygen at 0 °C can not have 24 L volume at 0.937 atm pressure. Have you copied it correctly?

ehild
 

1. How is work calculated in an isothermal compression process?

In an isothermal compression process, work is calculated as the product of the pressure and the change in volume. This is represented by the equation W = PΔV, where W is the work, P is the pressure, and ΔV is the change in volume.

2. What is the significance of an isothermal compression process in thermodynamics?

An isothermal compression process is significant in thermodynamics because it occurs at a constant temperature. This allows for the calculation of work without having to consider the change in internal energy, making it easier to analyze and understand.

3. How does an isothermal compression process differ from an adiabatic compression process?

In an isothermal compression process, the temperature remains constant, while in an adiabatic compression process, there is no heat exchange and the temperature can change. Additionally, work is only calculated using pressure and volume in an isothermal process, while in an adiabatic process, it also involves the change in temperature.

4. What are some real-world applications of isothermal compression?

One common real-world application of isothermal compression is in the operation of refrigerators and air conditioners. These devices use a combination of isothermal and adiabatic compression to cool a space by removing heat from the air and releasing it outside. Isothermal compression is also used in the compression stage of gas turbine engines.

5. How can isothermal compression be achieved in practice?

In theory, isothermal compression can be achieved by performing the process very slowly, allowing enough time for heat to dissipate and the temperature to remain constant. In practice, this is difficult to achieve, so engineers use different techniques, such as intercooling and heat exchange, to maintain a constant temperature as much as possible during the compression process.

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