Reversible Adiabatic Expansion for an Ideal Gas

In summary, for a monoatomic gas undergoing reversible expansion from 30 L and 400K to 60 L with a molar heat capacity of (3/2)R, independent of temperature, the final pressure is 0.55 atm and the final temperature remains at 400 K as the process is adiabatic. The equation Q=0 is used to solve for the final pressure and the equation P1V1= P2V2 is not applicable for an adiabatic process.
  • #1
adiabaffled
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Homework Statement


1 mole of a monoatomic gas undergoes reversible expansion from 30 L and 400K to 60 L. The molar heat capacity in this situation is (3/2)R, independent of temperature. Calculate the final pressure and temperature of this process if it is adiabatic.

Homework Equations


Q= 0 if it is adiabatic
Q= nCv(dT)
PV=nRT
P1V1= P2V2
monoatomic Cv= (3/2)R <-- heat capacity at const. vol.

The Attempt at a Solution


Using Q=0, 0= nCv(dT)
0= (1 mol)(3/2)(R)(dT)
dT= 0
P1V1=nRT or (P1)(30L)=(1)(8.314 J/mol K)(400 K)
P1= 1.1 atm (using conversion factor)
Substituting into P1V1=P2V2, I get 0.55 atm.
Temperature is still 400 K at the end

I wanted to make sure if this was correct (the fact that the change in temp is zero while it was adiabatic confused me).
 
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adiabaffled said:
P1V1= P2V2
That's for an isothermal process, but this one is adiabatic. There is a different, but similar-looking, equation to use instead.
 
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FAQ: Reversible Adiabatic Expansion for an Ideal Gas

What is reversible adiabatic expansion for an ideal gas?

Reversible adiabatic expansion for an ideal gas is a process in which an ideal gas expands without any heat transfer and without any energy losses. This process is also known as isentropic expansion.

What is the equation for reversible adiabatic expansion?

The equation for reversible adiabatic expansion is given by: PV^γ = constant, where P is the pressure, V is the volume, and γ is the adiabatic index (also known as the ratio of specific heats).

What is the difference between reversible adiabatic expansion and irreversible adiabatic expansion?

The main difference between reversible adiabatic expansion and irreversible adiabatic expansion is that reversible expansion occurs at a slow and controlled rate, while irreversible expansion occurs quickly and is not controlled. Additionally, reversible expansion results in no energy losses, while irreversible expansion results in energy losses due to friction and other factors.

What is the significance of reversible adiabatic expansion in thermodynamics?

Reversible adiabatic expansion is significant in thermodynamics because it is a theoretical process that can be used to measure the maximum amount of work that can be extracted from a system. It is also a key concept in understanding the principles of heat engines and refrigeration cycles.

What are some real-life examples of reversible adiabatic expansion?

Some real-life examples of reversible adiabatic expansion include the compression and expansion of air in a bicycle pump, the expansion of gases in a jet engine, and the compression and expansion of gases in a refrigerator or air conditioner.

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