What is the change in entropy ΔS of the gas?

In summary, the problem involves the calculation of entropy change for two moles of an ideal gas undergoing a reversible isothermal expansion. The integral method is suggested, using the ideal gas equation of state to simplify the expression. The final integral to be solved is \int_{V_{1}}^{V_{2}} \frac{PdV}{T} .
  • #1
kolua
69
3

Homework Statement


Two moles of an ideal gas undergo a reversible isothermal expansion from 3.37×10−2m3 to 4.29×10−2m3 at a temperature of 29.6 ∘C.

What is the change in entropy ΔS of the gas?

Homework Equations


pV=nRT

The Attempt at a Solution


W=∫V2V1pdV,

I don't know how to use this integral. And is it necessary to use this integral here? It seems like it is making the calculation more complicated than it should be. I have no other idea on how to approach this question. Please give me some hints!
 
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  • #2
Hint: In the integration, P=nRT/V
 
  • #3
You're on the right path. Note that the integral should be
[tex] \int_{V_{1}}^{V_{2}} \frac{PdV}{T} [/tex]
Manipulate the integrand using the ideal gas equation of state to obtain an expression in terms of the variable of integration (i.e. the volume) and then do the integral.
 

1. What is entropy and why is it important in relation to gas?

Entropy is a measure of the disorder or randomness in a system. In the context of gas, it refers to the distribution of gas molecules and their energy within a given space. Entropy is important because it helps us understand the behavior and properties of gases, such as their tendency to expand and fill any available space.

2. How is the change in entropy of a gas calculated?

The change in entropy (ΔS) of a gas can be calculated using the formula ΔS = Q/T, where Q is the amount of heat added or removed from the gas and T is the temperature at which the change occurs. This formula is based on the second law of thermodynamics, which states that the total entropy of a closed system can never decrease over time.

3. What factors can cause a change in entropy of a gas?

There are several factors that can cause a change in entropy of a gas, including changes in temperature, pressure, and volume. Additionally, any processes that involve energy transfer, such as chemical reactions or phase changes, can also result in a change in entropy.

4. How does the change in entropy of a gas affect its behavior?

Generally, an increase in entropy will result in a more disordered and less predictable behavior of the gas. This can lead to the gas expanding to fill a larger space or mixing with other gases. On the other hand, a decrease in entropy can cause the gas to become more ordered and potentially undergo a phase change.

5. Can the change in entropy of a gas be negative?

Yes, the change in entropy of a gas can be negative. This means that the gas has become more ordered and less random, which is often seen in processes such as condensation or freezing. However, the overall entropy of the universe must still increase, as per the second law of thermodynamics.

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