Numerical on adiabatic expansion

In summary, adiabatic expansion is a process in thermodynamics where a gas expands without gaining or losing heat to its surroundings, resulting in a decrease in temperature. It is an important process in various industrial and natural processes and can be calculated using the ideal gas law. The factors that affect adiabatic expansion include initial temperature and pressure, volume, gas type, and the presence of external work or heat. Adiabatic expansion differs from isothermal expansion in that it occurs without any exchange of heat with the surroundings, resulting in greater changes in temperature and internal energy.
  • #1
naimagul
10
0
An ideal gas with g =1.5 is expanded adiabatically. How many times has the gas to be expanded to reduce the rms velocity of molecules 2 times?
 
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  • #2
rms speed = √(3kT/m), where k is the Boltzmann constant and m the mass of one molecule.
So to halve the speed you need 1/4 of the absolute temperature.
For adiabatic process, T.V[itex]^{γ-1}[/itex] = constant
With γ = 1.5 you'd need 16 times the volume.
 
  • #3
Thanks for your help. It was great solving the problem.
 

Question 1: What is adiabatic expansion?

Adiabatic expansion is a process in thermodynamics where a gas expands without gaining or losing heat to its surroundings. This means that the temperature of the gas decreases as it expands.

Question 2: Why is adiabatic expansion important?

Adiabatic expansion is important because it is a fundamental process in many industrial and natural processes, such as in engines and in atmospheric dynamics. It also plays a crucial role in the study of thermodynamics and gas laws.

Question 3: How is adiabatic expansion calculated?

Adiabatic expansion can be calculated using the ideal gas law, which states that the pressure, volume, and temperature of a gas are related by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

Question 4: What are the factors that affect adiabatic expansion?

The factors that affect adiabatic expansion include the initial temperature and pressure of the gas, the volume of the container, and the type of gas. Additionally, the presence of external work or heat can also affect the process.

Question 5: How is adiabatic expansion different from isothermal expansion?

Adiabatic expansion differs from isothermal expansion in that adiabatic expansion occurs without any exchange of heat with the surroundings, while isothermal expansion occurs at a constant temperature. This means that adiabatic expansion has a greater change in temperature and internal energy compared to isothermal expansion.

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