In an internal combustion engine, air at atmospheric pressure and a temperature of about 20 ∘C is compressed in the cylinder by a piston to 18.0 of its original volume (compression ratio 8.0).
\Estimate the temperature of the compressed air, assuming the pressure reaches 38 atm .
\At temperature ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=9ff2b90cfb36cbcc0783ef73b9fe33f6.png\")
: \ \
Atmospheric pressure of the air is 1 atm. \ \
\Let initial volume of the air be ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=9c61c3473f57853f9cc2f81956b07ba6.png\")
.
Initial temperature ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=9ff2b90cfb36cbcc0783ef73b9fe33f6.png\")
of the air = 20°C = 20+273 = 293 K.
At temperature ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=091a436b980d1b0cad27bdff12be0389.png\")
:
Volume of the air is compressed by a factor of ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=43dea413dd50a99636aa53a509b0b511.png\")
, then volume is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=dcce281229a2ac8a46e53737292af69a.png\")
.
The atmospheric pressure of the gas at final temperature is 38 atm.
\Equation of the ideal gas: ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=d6d91ada44f43be36080f1ee747c7c52.png\")
.
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=999ef2bff27d0f45f22ab569065ecf24.png\")
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=1314b49a9a76dc89a67c3fd0f3277310.png\")
The Temperature of the gas is 1118.75°C.
\