How to calculate initial pressure and temperature - adiabatic process

In summary, the adiabatic equation states that the work done on a substance is the difference in the internal energy of the substance at the initial and final states. To find adiabatic work, you either need to know the change in temperature or the initial pressure. For this problem, the final pressure and final volume were used to calculate the work.
  • #1
JoeyBob
256
29
Homework Statement
Ratio from specific heats = 5/3

Initial volume = 0.814, final volume = 0.37, final pressure = 276000, final temperature is 297.273 K

Find Work
Relevant Equations
PV=nRT
Im confused on working backwards so to speak to find adiabatic work.

To find work for this adiabatic process, I either need to know the change in temperature OR the initial pressure (I think?).

The issue is that I don't know either the initial temperature nor the initial pressure so I am not sure how to calculate the work using the adiabatic eqns that require these values.

I know the answer to this problem is -63000 J, just not sure how to get there.
 
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  • #2
When you say adiabatic equations, what do mean?
 
  • #4
Are you familiar with the equation $$PV^{\gamma}=Constant$$
 
  • #5
JoeyBob said:
The issue is that I don't know either the initial temperature nor the initial pressure so I am not sure how to calculate the work using the adiabatic eqns that require these values.
The adiabatic equations you pointed me to don't involve temperature. Can you find the value of ##K##?
 
  • #6
JoeyBob said:
Homework Statement:: Ratio from specific heats = 5/3

Initial volume = 0.814, final volume = 0.37, final pressure = 276000, final temperature is 297.273 K

Find Work
Relevant Equations:: PV=nRT

Im confused on working backwards so to speak to find adiabatic work.

To find work for this adiabatic process, I either need to know the change in temperature OR the initial pressure (I think?).

The issue is that I don't know either the initial temperature nor the initial pressure so I am not sure how to calculate the work using the adiabatic eqns that require these values.

I know the answer to this problem is -63000 J, just not sure how to get there.
Check very carefully what you are given at final state.
 
  • #7
Chestermiller said:
Are you familiar with the equation $$PV^{\gamma}=Constant$$
So I use final volume and pressure for this? I treid that and it didnt give the right answer for me.
 
  • #8
JoeyBob said:
So I use final volume and pressure for this? I treid that and it didnt give the right answer for me.
Show us what you did.
 

FAQ: How to calculate initial pressure and temperature - adiabatic process

How do you calculate initial pressure and temperature in an adiabatic process?

In an adiabatic process, the initial pressure and temperature can be calculated using the ideal gas law, which states that PV = nRT. This equation relates the pressure (P), volume (V), number of moles (n), and temperature (T) of an ideal gas. In an adiabatic process, there is no heat exchange, so the change in internal energy (ΔU) is equal to 0. This means that the equation can be simplified to P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

What is the difference between initial and final pressure and temperature in an adiabatic process?

The initial pressure and temperature refer to the values at the beginning of the adiabatic process, while the final pressure and temperature refer to the values at the end of the process. In an adiabatic process, the initial and final values are related by the ideal gas law, where the initial pressure and volume are inversely proportional to the final pressure and volume.

Can the initial pressure and temperature be calculated if the final pressure and temperature are known?

Yes, the initial pressure and temperature can be calculated if the final pressure and temperature are known. This can be done by rearranging the ideal gas law equation to solve for the initial pressure and temperature. Keep in mind that the number of moles and volume of the gas must remain constant in an adiabatic process.

How does an adiabatic process affect the pressure and temperature of a gas?

In an adiabatic process, the pressure and temperature of a gas are inversely proportional. This means that as the volume of the gas decreases, the pressure increases, and the temperature also increases. Conversely, as the volume of the gas increases, the pressure decreases, and the temperature also decreases. This relationship is described by the ideal gas law.

What other factors can affect the initial pressure and temperature in an adiabatic process?

In addition to the ideal gas law, other factors that can affect the initial pressure and temperature in an adiabatic process include the specific heat capacity of the gas, the work done on or by the gas, and the type of process (e.g. isothermal, adiabatic, isobaric, isochoric). These factors can change the internal energy of the gas and therefore affect the initial and final pressure and temperature values.

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