Ideal gas adiabatic/isovolumetric help

In summary, an adiabatic process transfers zero heat. In a isobaric process, the pressure does not change, but the volume does. The entropy of the gas changes when it is compressed from an original volume of four times to its original size at a constant pressure.
  • #1
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Homework Statement


two moles of an ideal gas is initially at P = 2*20^5 Pa expands adiabaticaly to four times its original volume. it is then compressed at constant pressure to its original volume. what is the change in entropy of the gas

Cp = 20.78 joules/mole-deg
Cv = 12.47 joules/mole-deg
gamma = 5/3



Homework Equations



adiabatic expansion --> PV^gamma = constant, Q = 0
isovolumetric compression --> nCv(deltaT)
entropy deltaS= deltaQ/T

The Attempt at a Solution



i am not sure how to use the adiabatic equation because although P and V is given as well as gamma, i can solve for 'constant' but where does constant come into play?

since for an adiabat Q = 0, do i just take it as zero and move on or do i actually need to solve for something.

as for the isovolumetric compression, moles is given, Cv is given but not deltaT so i solved the Pv=nRT eq for T and subbed it in, i then assumed P and V to be constants as stated in the problem?? and solved for Q getting 1.5 joules

when i solved for entropy i did (compression - expansion, so isovolumetric minus adibat = i subbed in the equation from the isovolumetric equation in and canceled out the T's and was able to get deltaS = 24.94 joules per kelvin

did i take the correct approach? help appreciated...
 
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  • #2
As you have recognized, the heat transferred in an adiabatic process is zero. Therefore, the ratio of Q/T is zero, and there is no change in entropy.

And the second process is at constant pressure (isobaric), not constant volume, so use Cp in the second equation.

You need to find the two temperatures, and for that you need to find the pressure after the adiabatic expansion. That's where the gamma equation comes in. (You said volume is given but you did not state what initial volume is). Once you have the pressure after the expansion, you can get the temperature simply using PV=nRT

Then find the delta T for the isobaric compression.

And to find the delta S, you need a slightly different formula, since T is not constant (look for a natural log formula).
 
  • #3
hi thanks, just to clarify the problem does not specify an actual volume just the amount at which it decreases/increased
 

FAQ: Ideal gas adiabatic/isovolumetric help

What is an ideal gas?

An ideal gas is a theoretical concept in which gas particles have no volume and do not interact with each other. It follows the Ideal Gas Law, which states that the pressure, volume, and temperature of an ideal 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.

What is an adiabatic process?

An adiabatic process is a thermodynamic process in which there is no heat exchange between the system and its surroundings. This means that the change in internal energy of the system is equal to the work done on or by the system. In the context of ideal gases, this can occur when a gas expands or compresses without any heat transfer.

What is an isovolumetric process?

An isovolumetric process, also known as an isochoric process, is a thermodynamic process in which the volume of the system remains constant. This means that no work is done by or on the system, so the change in internal energy is equal to the heat added or removed from the system. In the context of ideal gases, this can occur when the gas is heated or cooled at a constant volume.

How are adiabatic and isovolumetric processes related?

Adiabatic and isovolumetric processes are related in that they both involve no heat transfer and result in a change in the internal energy of the system. However, adiabatic processes involve a change in volume while isovolumetric processes involve a change in temperature.

How can I calculate the temperature change in an adiabatic or isovolumetric process?

The temperature change in an adiabatic or isovolumetric process can be calculated using the ideal gas law. In an adiabatic process, the temperature change can be found using the equation T2/T1 = (V1/V2)^(gamma-1), where T1 and T2 are the initial and final temperatures, V1 and V2 are the initial and final volumes, and gamma is the adiabatic index. In an isovolumetric process, the change in temperature can be found using the equation T2/T1 = P2/P1, where P1 and P2 are the initial and final pressures.

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