Adiabatic Expansion of Gas: Does the Number of Moles Affect the Calculation?

In summary, the adiabatic factor gamma for 1 mole of gas is determined by the ratio of molar heat capacities Cp,m and Cv,m. This calculation remains the same for 2 moles of gas and does not depend on the number of moles. This is because the n in the equation n Cp,m / n Cv,m cancels out, making the calculation independent of n. Therefore, the adiabatic expansion of gas is the same for 1 mole and 100 moles.
  • #1
quietrain
655
2
for 1 mole of gas, the adiabatic factor gamma is given by Cp,m / Cv,m
where the C are molar heat capacities

so if now i have 2 moles of gas

will my calculation change at all?

for example, if i use PVgamma = PVgamma

will anything change? it seems weird, it doesn't depend on the number of moles n

since n Cp,m / n Cv,m , the n cancels out

issn't this akin to saying adiabatic expansion of gas is the same for 1 mole VS 100 moles?
 
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  • #2
Hi.

quietrain said:
for 1 mole of gas, the adiabatic factor gamma is given by Cp,m / Cv,m
where the C are molar heat capacities

so if now i have 2 moles of gas

will my calculation change at all?

for example, if i use PVgamma = PVgamma

will anything change? it seems weird, it doesn't depend on the number of moles n

since n Cp,m / n Cv,m , the n cancels out

issn't this akin to saying adiabatic expansion of gas is the same for 1 mole VS 100 moles?

Do not worry about moles n. Calculation of physical quantity per mole do not depend on n.

Regards.
 
  • #3
alright thanks!
 

What is adiabatic expansion of gas?

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

What causes adiabatic expansion?

Adiabatic expansion occurs when a gas is allowed to expand freely, without any external heat or work being added to the system. This could happen, for example, when a gas is released from a pressurized container into a larger volume.

What is the equation for adiabatic expansion?

The equation for adiabatic expansion is P1V1^γ = P2V2^γ, 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 (also known as the heat capacity ratio).

How does adiabatic expansion differ from isothermal expansion?

Unlike adiabatic expansion, isothermal expansion is a process in which a gas expands at a constant temperature. This means that the gas must exchange heat with its surroundings in order to maintain a constant temperature. In contrast, adiabatic expansion does not involve any heat exchange.

What are some real-world applications of adiabatic expansion?

Adiabatic expansion is an important concept in thermodynamics and is used in various fields, including meteorology (to explain changes in air temperature and pressure), engineering (in the design of engines and turbines), and chemistry (to study chemical reactions that occur without heat exchange). It is also used in refrigeration and air conditioning systems to cool air by allowing it to expand without heat exchange.

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