Adiabatic Expansion of a Gas: Final Pressure-Volume Product Calculation

In summary, the given problem involves an adiabatic expansion of a gas consisting of diatomic molecules with 3 degrees of freedom. The final PV (pressure volume) product is calculated to be 25590 Pa/m3. However, there may be a possibility of approaching the problem incorrectly or an error in the answer.
  • #1
vetgirl1990
85
3

Homework Statement


A gas consisting of diatomic molecules that can rotate but not oscillate at a given range of temperatures expands adiabatically from pressure of 365Pa and volume of 70m3, doing 101J of work, while expanding to a final volume. What is its final PV (pressure volume) product?

Homework Equations


For an adiabatic expansion:
W = (1/ϒ-1)(pfvf - pivi)

The Attempt at a Solution


i) Degrees of freedom: 3
Therefore, ϒ=1.4

ii) Plug and chug of the equation above.
W = (1/ϒ-1)(pfvf - pivi)
101 = (1/1.4-1)(pfvf - 365*70)
101 = 2.5pfvf - 63875
pfvf = 25590 Pa / m3

I'm fairly certain I found the degrees of freedom correctly, and the latter part of my calculations is pretty straightforward... Still getting the wrong answer, however. Chance that the answer is wrong? Or am I approaching the problem incorrectly?
 
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  • #2
Isn't it 3 degrees of freedom for a monatomic gas?
 

1. What is adiabatic expansion of a gas?

Adiabatic expansion of a gas is a process in which a gas expands without any heat being added or removed from the system. This means that the temperature of the gas decreases as it expands, while the internal energy remains constant.

2. How does adiabatic expansion differ from isothermal expansion?

Adiabatic expansion differs from isothermal expansion in that isothermal expansion occurs at a constant temperature, while adiabatic expansion occurs without any heat exchange with the surroundings. This results in a change in temperature for adiabatic expansion, while the temperature remains constant for isothermal expansion.

3. What is the equation for adiabatic expansion?

The equation for adiabatic expansion is P1V1γ = P2V2γ, where P1 and V1 are the initial pressure and volume of the gas, P2 and V2 are the final pressure and volume of the gas, and γ is the adiabatic index or ratio of specific heats.

4. What is the significance of the adiabatic index?

The adiabatic index, also known as the ratio of specific heats, is a measure of how much a gas's internal energy changes as its temperature changes. It is a constant value for a particular gas and is used in the adiabatic expansion equation to calculate the change in volume of the gas.

5. What are some real-world applications of adiabatic expansion?

Adiabatic expansion is used in various real-world applications, including the operation of internal combustion engines, gas turbines, and refrigeration systems. It is also an important concept in thermodynamics and is used to study the behavior of gases in various systems, such as in weather patterns and atmospheric dynamics.

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