# The ideal gas law for an adiabatic process

• garyd
In summary: BIGUOUS CONVERSATIONIn summary, a diesel engine requires no spark plug; instead the air in the cylinder is compresses so highly the fuel ignites spontaneously on injection to the cylinder.
garyd

## Homework Statement

Hi can someone please have a look at this question and let me know if I am on the right track, thanks.

A diesel engine requires no spark plug; instead the air in the cylinder is compresses so highly the fuel ignites spontaneously on injection to the cylinder.

Q. If the air is initially at 293K and then is compressed adiabatically by a factor of 15, what final temperature is attained ?( Just prior to injection, also consider air as an ideal gas)
Variables:
T1=293K
V1= 1
V2=1/15
T2=?

## Homework Equations

T1 *V1^(Ƴ-1) = T2* V2^(Ƴ-1)

## The Attempt at a Solution

Above relationship applies as process is adiabatic?

293× (1^(1.4-1)/ (1/15^(1.4-1) ))=866K

Last edited:
Looks good to me. Why the doubtful question mark ?

1 person
BvU said:
Why the doubtful question mark ?

Confidence, I am learning to trust the equations.

Another part of the question is; by what factor has the pressure increased? Can I use P V^Ƴ=constant, with p1=1, multiplied by ratio of V1/V2, both to the power of Ƴ? ans=2.95

Re post 1: T1 *V1^(Ƴ-1) = T1* V1^(Ƴ-1) I read T1 *V1^(Ƴ-1) = T2* V2^(Ƴ-1) which looks good.

Re post 3: numerically I get something different, but then I use ##\gamma##, not ##\gamma -1## as the exponent... Big difference !

1 person
Re post 3: numerically I get something different said:
Yes I was using wrong exponent, 44 is the correct factor, thanks.

garyd said:
Confidence, I am learning to trust the equations.

Another part of the question is; by what factor has the pressure increased? Can I use P V^Ƴ=constant, with p1=1, multiplied by ratio of V1/V2, both to the power of Ƴ? ans=2.95

Once you have the temperature worked out, just use the ideal gas law: PV=nRT

P1V1/T1 = P2V2/T2

P2/P1 = (V1/V2)(T2/T1)

AM

1 person

## 1. What is the ideal gas law for an adiabatic process?

The ideal gas law for an adiabatic process is a combination of the ideal gas law and the first law of thermodynamics. It states that in a closed system, the pressure and volume of an ideal gas are inversely proportional to each other when the process is adiabatic, meaning there is no heat exchange with the surroundings.

## 2. How is the ideal gas law for an adiabatic process derived?

The ideal gas law for an adiabatic process is derived by combining the ideal gas law, which describes the relationship between pressure, volume, and temperature of an ideal gas, with the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

## 3. What are the assumptions made in the ideal gas law for an adiabatic process?

The ideal gas law for an adiabatic process assumes that the gas is ideal, meaning it follows the ideal gas law, and that the process is adiabatic, meaning there is no heat exchange with the surroundings. It also assumes that the gas is in a closed system and that there is no change in the number of moles of gas.

## 4. What is the significance of the ideal gas law for an adiabatic process?

The ideal gas law for an adiabatic process is significant because it helps us understand the behavior of ideal gases in a closed system where there is no heat exchange. It allows us to predict how changes in pressure, volume, and temperature will affect each other in an adiabatic process and is used in various fields such as thermodynamics, chemistry, and engineering.

## 5. How is the ideal gas law for an adiabatic process used in real-life applications?

The ideal gas law for an adiabatic process is used in various real-life applications, such as in the design of internal combustion engines, where the adiabatic process of the gas inside the engine is used to calculate the work done by the engine. It is also used in the design of air compressors and refrigeration systems, where adiabatic processes are involved in the compression and expansion of gases.

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