Adiabatic Expansion: Solving for Pressure and Volume

In summary, adiabatic expansion is a process where a gas expands without any heat being added or removed from the system, keeping the internal energy constant. It differs from isothermal expansion, where the temperature remains constant. The equation for adiabatic expansion is P1V1^γ = P2V2^γ, and it can be used to solve for pressure and volume by plugging in initial values and the adiabatic index. Real-world examples of adiabatic expansion include gas expansion in piston-cylinder systems, tires, refrigerators, and heat engines.
  • #1
bobsmith76
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Homework Statement



see attachment





The Attempt at a Solution



I'm having trouble where they multiply (101,000 by 1.5 m3)5/3

I get 151,500 Pa*m5
not 199,000 Pa*m5
 

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  • #2
bobsmith76 said:

Homework Statement



see attachment

The Attempt at a Solution



I'm having trouble where they multiply (101,000 by 1.5 m3)5/3

I get 151,500 Pa*m5
not 199,000 Pa*m5
The adiabatic condition is:

[itex]PV^\gamma = K[/itex] which means [itex]P^1 \times V^\gamma = K[/itex]

Since [itex]\gamma = 5/3[/itex], and V = 1.5, [itex]V^\gamma = 1.5^{5/3} = 1.97[/itex]

AM
 

What is adiabatic expansion?

Adiabatic expansion is a process in thermodynamics where a gas expands without any heat being added or removed from the system. This means that the internal energy of the gas remains constant during the expansion.

How is adiabatic expansion different from isothermal expansion?

In adiabatic expansion, no heat is transferred between the gas and its surroundings, whereas in isothermal expansion, the temperature of the gas remains constant throughout the expansion. This means that in adiabatic expansion, the gas experiences a change in temperature, while in isothermal expansion, the gas experiences a change in volume.

What is the equation for adiabatic expansion?

The equation for adiabatic expansion is P1V1γ = P2V2γ, where P is pressure, V is volume, and γ is the adiabatic index. This equation represents the relationship between pressure and volume during adiabatic expansion.

How do you solve for pressure and volume in adiabatic expansion?

To solve for pressure and volume in adiabatic expansion, you can use the adiabatic expansion equation and plug in the initial values for pressure and volume, as well as the adiabatic index. Then, you can solve for the final values of pressure and volume.

What are some real-world examples of adiabatic expansion?

Some real-world examples of adiabatic expansion include the expansion of a gas in a piston-cylinder system, the expansion of air in a tire, and the expansion of gas in a cooling system of a refrigerator. Adiabatic expansion is also used in the compression and expansion processes in heat engines such as car engines and gas turbines.

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