Increase Entropy in Sealed, Thermally Insulated Container

In summary, the conversation discusses a sealed and thermally insulated container divided into two equal volumes by an impermeable wall. The left half of the container initially contains n moles of an ideal gas at temperature T. The question is posed about the change in entropy of the system when the wall is suddenly removed and the gas expands to fill the entire volume. One individual mentions an equation for entropy in terms of temperature and volume, and another asks for the source of this equation.
  • #1
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A sealed and thermally insulated container of total volume V is divided into two equal volumes by an impermeable wall. The left half of the container is initially occupied by n moles of an ideal
gas at temperature T. Which of the following gives the change in entropy of the system when
the wall is suddenly removed and the gas expands to fill the entire volume?

thermo is a very weak subject for me... any help is appreciated

I know that entropy is s=k*g where g is the number of accessible states, but I'm not sure where to go from here
 
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  • #2
[tex] \Delta S(T,P)=\frac{3}{2}Nk ln( \frac{T_2}{T_1} ) + Nk ln( \frac{V_2}{V_1} )[/tex]

This is the state equation for the entropy in terms of temperature and volume. Since the container is thermally insulated, T2=T1 and the first term drops out since ln(1)=0. Since V2 > V1, the second term is positive and the entropy of the system will INCREASE.
 
  • #3
where did you get this equation from? Is this a standard equation?
 
  • #4
Look under the entropy section here:http://en.wikipedia.org/wiki/Ideal_gas"
 
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1. How does a sealed, thermally insulated container increase entropy?

The second law of thermodynamics states that entropy, or disorder, will always increase in a closed system. In a sealed, thermally insulated container, the heat energy from the surroundings is unable to escape, causing the molecules within the container to move and interact with each other more randomly, thus increasing the entropy.

2. What factors affect the rate of entropy increase in a sealed, thermally insulated container?

The rate of entropy increase in a sealed, thermally insulated container is affected by the temperature, pressure, and composition of the substances inside the container. Higher temperatures and pressures, as well as a larger number of molecules, will lead to a faster increase in entropy.

3. How can the increase of entropy in a sealed, thermally insulated container be measured?

One way to measure the increase of entropy in a sealed, thermally insulated container is by calculating the change in temperature over time. As the entropy increases, the temperature inside the container will also increase due to the increased molecular movement. Another method is to measure the change in pressure, as the increased molecular movement will lead to a higher pressure inside the container.

4. Can the increase of entropy in a sealed, thermally insulated container be reversed?

No, the increase of entropy in a sealed, thermally insulated container cannot be reversed. The second law of thermodynamics states that entropy will always increase in a closed system, and it is impossible to completely eliminate all molecular movement and restore the system to a state of low entropy.

5. Are there any practical applications for understanding the increase of entropy in sealed, thermally insulated containers?

Yes, understanding the principles of entropy and how it increases in sealed, thermally insulated containers is crucial in various industries such as food preservation, insulation materials, and refrigeration. By controlling and managing the increase of entropy, we can improve the efficiency and effectiveness of these processes.

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