Adiabatic expansion of an ideal gas.

In summary, the entropy change of a diatomic ideal gas that expands from pressure P and volume V to pressure 2P and volume 4V can be calculated using the equation ΔS = nRln(V2/V1), where n is the number of moles and R is the gas constant. The value of R is 8.314 J K−1 mol−1, and in this case, n = 1. The final result is 8.314 J K−1 mol−1 ln(4), which is equal to 33.256 J K−1 mol−1. This is the entropy change of the gas in the process.
  • #1
Rekabnire
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Problem: One mole of a diatomic ideal gas, initially having pressure P and volume V, expands so as to have pressure 2P and volume 4V. Determine the entropy change of the gas in the process.


Attempt: I thought this would just be R ln(V2/V1)... So, I said (8.314)*ln(4) but it's wrong...
There's an example almost exactly like it in my textbook, and I don't see where I'm going wrong. The example they use just leaves the answer as 4R... Could I be using the wrong value for R?

I have a feeling that PV^gamma fits in there somehow, since we're given the fact that it's diatomic (gamma=1.4), but I don't know how... R ln(V2/V1) is an expression for the entropy change for an adiabatic process, right?
 
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  • #2
Solution: The entropy change of the gas in the process can be calculated using the equation ΔS = nRln(V2/V1). In this case, n = 1 and R = 8.314 J K−1 mol−1, so the entropy change is 8.314 J K−1 mol−1 ln(4). Therefore, the entropy change of the gas in the process is 33.256 J K−1 mol−1.
 

1. What is adiabatic expansion?

Adiabatic expansion is a process in which an ideal gas expands without any heat being added or removed from the system. This means that the gas does work on its surroundings without exchanging heat with them.

2. Why is adiabatic expansion important?

Adiabatic expansion is important because it can help us understand and predict the behavior of gases in various systems, such as in internal combustion engines and in weather systems. It also plays a crucial role in thermodynamics and in the study of heat and energy.

3. What is an ideal gas?

An ideal gas is a theoretical gas that follows the ideal gas law, which describes the relationship between pressure, volume, temperature, and number of moles for a gas. It assumes that there are no intermolecular forces between gas particles and that the particles themselves have no volume.

4. How is adiabatic expansion different from isothermal expansion?

The main difference between adiabatic and isothermal expansion is that adiabatic expansion occurs without any heat exchange, while isothermal expansion occurs at a constant temperature. This means that adiabatic expansion leads to a change in temperature, while isothermal expansion does not.

5. What are some real-life examples of adiabatic expansion?

Some real-life examples of adiabatic expansion include the expansion of gases in a combustion engine, the expansion of air in a bicycle pump, and the expansion of air in a balloon as it rises in the atmosphere. Weather systems, such as hurricanes and thunderstorms, also involve adiabatic expansion of air masses.

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