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Thanks Jon
This might help some of you, smarter than me, people
Lol
(Resource: Wikipedia online)
Example of adiabatic compression
The compression stroke in a gasoline engine can be used as an example of adiabatic compression. The simplifying assumptions are: the uncompressed volume of the cylinder is 1000 cm3 (one litre); the gas within is nearly pure nitrogen (thus a diatomic gas with five degrees of freedom and so \gamma = 7/5); the compression ratio of the engine is 10:1 (that is, the 1000 cm3 volume of uncompressed gas be reduced to 100 cm3 by the piston); and that the uncompressed gas is at approximately room temperature and pressure (a warm room temperature of ~27 °C or 300 K, and a pressure of 1 bar ~ 100 kPa, or about 14.7 PSI, i.e. typical sea-level atmospheric pressure).
P V^{\gamma} = \operatorname{constant} = 100,000 \operatorname{pa} \times 1000^{7/5} = 100 \times 10^3 \times 15.8 \times 10^3 = 1.58 \times 10^9
so our adiabatic constant for this example is about 1.58 billion.
The gas is now compressed to a 100 cm3 volume (we will assume this happens quickly enough that no heat can enter or leave the gas). The new volume is 100 cm3, but the constant for this experiment is still 1.58 billion:
P V^{\gamma} = \operatorname{constant} = 1.58 \times 10^9 = P \times 100^{7/5}
so solving for P:
P = 1.58 \times 10^9 / {100^{7/5}} = 1.58 \times 10^9 / 630.9 = 2.50 \times 10^6 \operatorname{ Pa}
or about 362 PSI or 24.5 atm. Note that this pressure increase is more than a simple 10:1 compression ratio would indicate; this is because the gas is not only compressed, but the work done to compress the gas also increases its internal energy which manifests itself by a rise in the gas's temperature and an additional rise in pressure above what would result from a simplistic calculation of 10 times the original pressure.
We can solve for the temperature of the compressed gas in the engine cylinder as well, using the ideal gas law, PV=RT (R the specific gas constant for that gas). Our initial conditions are 100,000 pa of pressure, 1000 cm3 volume, and 300 K of temperature, so our experimental constant is:
{P V \over T} =\operatorname {constant} = {{10^5 \times 10^3 } \over {300} } = 3.33 \times 10^5
We know the compressed gas has V = 100 cm3 and P = 2.50E6 pascals, so we can solve for temperature by simple algebra:
{P V \over {\operatorname{constant}}} = T = {{2.50 \times 10^6 \times 100} \over {3.33 \times 10^5}} = 751
That is a final temperature of 751 K, or 477 °C, or 892 °F, well above the ignition point of many fuels. This is why a high compression engine requires fuels specially formulated to not self-ignite (which would cause engine knocking when operated under these conditions of temperature and pressure), or that a supercharger with an intercooler to provide a pressure boost but with a lower temperature rise would be advantageous. A diesel engine operates under even more extreme conditions, with compression ratios of 20:1 or more being typical, in order to provide a very high gas temperature which ensures immediate ignition of the injected fuel.
https://en.m.wikipedia.org/wiki/Adiabatic_process
Thanks Jon
This might help some of you, smarter than me, people
Lol
(Resource: Wikipedia online)
Example of adiabatic compression
The compression stroke in a gasoline engine can be used as an example of adiabatic compression. The simplifying assumptions are: the uncompressed volume of the cylinder is 1000 cm3 (one litre); the gas within is nearly pure nitrogen (thus a diatomic gas with five degrees of freedom and so \gamma = 7/5); the compression ratio of the engine is 10:1 (that is, the 1000 cm3 volume of uncompressed gas be reduced to 100 cm3 by the piston); and that the uncompressed gas is at approximately room temperature and pressure (a warm room temperature of ~27 °C or 300 K, and a pressure of 1 bar ~ 100 kPa, or about 14.7 PSI, i.e. typical sea-level atmospheric pressure).
P V^{\gamma} = \operatorname{constant} = 100,000 \operatorname{pa} \times 1000^{7/5} = 100 \times 10^3 \times 15.8 \times 10^3 = 1.58 \times 10^9
so our adiabatic constant for this example is about 1.58 billion.
The gas is now compressed to a 100 cm3 volume (we will assume this happens quickly enough that no heat can enter or leave the gas). The new volume is 100 cm3, but the constant for this experiment is still 1.58 billion:
P V^{\gamma} = \operatorname{constant} = 1.58 \times 10^9 = P \times 100^{7/5}
so solving for P:
P = 1.58 \times 10^9 / {100^{7/5}} = 1.58 \times 10^9 / 630.9 = 2.50 \times 10^6 \operatorname{ Pa}
or about 362 PSI or 24.5 atm. Note that this pressure increase is more than a simple 10:1 compression ratio would indicate; this is because the gas is not only compressed, but the work done to compress the gas also increases its internal energy which manifests itself by a rise in the gas's temperature and an additional rise in pressure above what would result from a simplistic calculation of 10 times the original pressure.
We can solve for the temperature of the compressed gas in the engine cylinder as well, using the ideal gas law, PV=RT (R the specific gas constant for that gas). Our initial conditions are 100,000 pa of pressure, 1000 cm3 volume, and 300 K of temperature, so our experimental constant is:
{P V \over T} =\operatorname {constant} = {{10^5 \times 10^3 } \over {300} } = 3.33 \times 10^5
We know the compressed gas has V = 100 cm3 and P = 2.50E6 pascals, so we can solve for temperature by simple algebra:
{P V \over {\operatorname{constant}}} = T = {{2.50 \times 10^6 \times 100} \over {3.33 \times 10^5}} = 751
That is a final temperature of 751 K, or 477 °C, or 892 °F, well above the ignition point of many fuels. This is why a high compression engine requires fuels specially formulated to not self-ignite (which would cause engine knocking when operated under these conditions of temperature and pressure), or that a supercharger with an intercooler to provide a pressure boost but with a lower temperature rise would be advantageous. A diesel engine operates under even more extreme conditions, with compression ratios of 20:1 or more being typical, in order to provide a very high gas temperature which ensures immediate ignition of the injected fuel.
https://en.m.wikipedia.org/wiki/Adiabatic_process
