Isothermally Expanding Question

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He is unsure of how to incorporate the information about the cylinder into the problem and is having difficulty making progress. Another user suggests using the ideal gas law to substitute for the constant temperature and using an integral to find the work done. In summary, Chetan is seeking help with a thermodynamics problem involving two moles of an ideal gas being compressed at a constant temperature, and another user suggests using the ideal gas law and an integral to find the work done.
  • #1
PsychonautQQ
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Homework Statement


Two moles of an ideal gas are compressed in a cylinder at a constant temperature at 338K until the original pressure is tripled. Calculate the amount of work done.



Homework Equations


PV=nRT
PV/T = c


The Attempt at a Solution


I don't know how to incorporate the cylinder information into this problem.. or get anywhere at all really.
3Pi = Pf
does this lead to Vi = 3Vf? since PV/T = c and T doesn't change?

W = PdV = nRdT..?
..halppp;-(
 
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  • #2
PsychonautQQ said:
3Pi = Pf
does this lead to Vi = 3Vf? since PV/T = c and T doesn't change?
Yes.

PsychonautQQ said:
W = PdV = nRdT..?
No, that doesn't make sense since P is not constant and T is.

You need the formula for work as an integral over dV and use the ideal gas law to substitute for T which is constant.
 
  • #3
If the temperature is constant, what is the ratio of the initial volume to the final volume? Your equation for the work is correct (if you use the convention that dW is the work done on the surroundings by the system). Just substitute nRT/V for P and integrate.

Chet
 

Related to Isothermally Expanding Question

What is an isothermally expanding question?

An isothermally expanding question is a type of question that involves a process in which the temperature remains constant while the volume or pressure changes.

What is the significance of an isothermally expanding question?

An isothermally expanding question is significant in thermodynamics and other fields of science as it allows for the analysis of how a system changes while maintaining a constant temperature.

What are some examples of isothermally expanding questions?

Some examples of isothermally expanding questions include: How does the volume of a gas change as its pressure decreases at a constant temperature? How does the temperature change as a solid expands in volume? How does the pressure of a liquid change as it is heated at a constant volume?

How is an isothermally expanding question different from an adiabatic question?

An isothermally expanding question involves a process where the temperature remains constant, while an adiabatic question involves a process where there is no heat exchange with the surroundings. In other words, an isothermally expanding question focuses on changes in volume or pressure while maintaining a constant temperature, while an adiabatic question focuses on changes in temperature without any heat transfer.

What are some real-world applications of isothermally expanding questions?

Isothermally expanding questions have many applications in fields such as thermodynamics, engineering, and chemistry. For example, they can be used to study the behavior of gases in a closed system, to determine the efficiency of heat engines, and to understand the properties of various materials under different conditions.

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