A Jaguar XK8 convertible has an eightcylinder engine At the

A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 500 cm3 of air at atmospheric pressure (1.01×105Pa) and a temperature of 27.0 C. At the end of the stroke, the air has been compressed to a volume of 46.5 cm3 and the gauge pressure has increased to 2.80×106 Pa .

Compute the final temperature.

Solution

The formula to use is

(PV/T)i = (PV/T)f

where

P = pressure
V = volume
T = temperature

and the subscripts \"i\" and \"f\" refer to the original and final conditions respectively.

In this problem, Tf is the unknown hence rearranging the above formula to solve for \"Tf\"

Tf = [(PfVf)/(PiVi)]Ti

NOTE:

Convert \"To\" to the Kelvin absolute scale before plugging it in the equation, i.e.,

Ti = 27 + 273 = 295 K

Substituting values,

Tf = [(2.80 x 10^6)(46.5)/(1.01 x 10^5)(500)]*295

Tf = 760 K

Tf = 737 - 273 = 487. C