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The air pressure inside the tube of a car tire is 353 kPa at a temperature...

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The air pressure inside the tube of a car tire is 353 kPa at atemperature of 14.0 Â°C. What is the pressure of the air, if thetemperature of the tire increases to 63.0 Â°C? Assume that thevolume of the tube doesn't change.
What is the air pressure inside the tube, if the volume of thetube is not constant, but it increases from 21.0 l to 21.9 l duringthe warming process described above?

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4.5 Ratings (697 Votes)

ans)

from above data that

given that

Initial pressure P = 353 Kpa

Initial temperature T = 14 ^o C

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 14 + 273

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 287 K

Final temperature T ' = 63^o C

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 63+ 273

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 336 K

At constant volume , P ' / P = T ' / T

From this P ' = (T' /T ) P

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 413.3 kPa

Initial volume V =Â Â 21.0 l

Final volume V ' = 21.9 l

From the relation PV = nRT

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â PV /T = constant

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â P'V'/T' = PV/TÂ Â Â Â

From this P ' = PVT' / V'T

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = (353*21.0*336) /(21.9 * 287 )

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 396.3 kPa

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