Find entropy change for free expantion of ideal gas

In summary: In the case of an ideal gas expanding into a larger volume in an isolated system, the energy and temperature remain the same, resulting in no change in entropy. However, when the gas expands into a larger volume while also having heat flow into it, the entropy increases due to the increased energy and temperature.
  • #1
klinke
1
0
entropy = jouls/kelvin
supose 1 liter of ideal gas is allowed to freely expand into a 2 liter volume in an isolated system
the energy in the system would remain the same,
the temperature in the system would remain the same
therefore if entropy =jouls/kelvin the entropy would remain the same
howerer if 1 liter of ideal gas is allowed to freely expand into a 2 liter volume in an isolated system the entropy does increase.
how dose entropy=jouls/kelvin ?
 
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  • #2
klinke said:
entropy = jouls/kelvin
supose 1 liter of ideal gas is allowed to freely expand into a 2 liter volume in an isolated system
the energy in the system would remain the same,
the temperature in the system would remain the same
therefore if entropy =jouls/kelvin the entropy would remain the same
howerer if 1 liter of ideal gas is allowed to freely expand into a 2 liter volume in an isolated system the entropy does increase.
how dose entropy=jouls/kelvin ?
ΔS = ∫dS = ∫dQ/T over a reversible path between the initial and final states.

The initial state is (P,V,T) and the final state is (P/2,2V,T). So to calculate the entropy change you have to find a reversible path between those two states. (hint: the reversible path involves work being done and heat flow into the gas).

AM
 

1. What is entropy change in the context of free expansion of an ideal gas?

The entropy change in free expansion of an ideal gas is the measure of the change in disorder or randomness of the gas particles during the expansion process.

2. How is entropy change calculated for free expansion of an ideal gas?

The entropy change for free expansion of an ideal gas is calculated using the formula ΔS = nRln(Vf/Vi), where ΔS is the entropy change, n is the number of moles of gas, R is the universal gas constant, Vf is the final volume, and Vi is the initial volume.

3. Does entropy always increase during free expansion of an ideal gas?

Yes, entropy always increases during free expansion of an ideal gas. This is because the particles of the gas are becoming more disordered as they expand into a larger volume.

4. What is the significance of calculating entropy change for free expansion of an ideal gas?

Calculating entropy change for free expansion of an ideal gas allows us to understand the thermodynamic properties of the gas and how it behaves under different conditions. It also helps in predicting the direction of spontaneous processes.

5. Can entropy change be negative for free expansion of an ideal gas?

No, entropy change cannot be negative for free expansion of an ideal gas. The second law of thermodynamics states that the total entropy of a closed system must always increase or remain constant, but it cannot decrease.

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