Question

A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499 cm3 of air at atmospheric pressure (1.01×105 Pa) and a temperature of 27.0∘C. At the end of the stroke, the air has been compressed to a volume of 46.2 cm3 and the gauge pressure has increased to 2.72×106 Pa.

Answer 1

Answer:

The final temperature is 503°C.

Explanation:

Given that,

Volume = 499 cm³

Gauge pressure $P_{i}= 1.01\times10^{5}\ Pa$

Temperature = 27.0°

Final volume = 46.2 cm³

Increased pressure $P_{f}= 2.72\times10^{6}\ Pa$

We need to calculate the temperature

Using ideal gas equation

$PV=nRT$

Rearrange equation

$T_{2}=\dfrac{P_{2}V_{2}}{P_{1}V_{1}}\timesT_{1}$

Put the value into the formula

$T_{2}=\dfrac{(2.72\times10^{6}+1.01\times10^{5})\times46.2\times10^{-6}}{1.01\times10^{5}\times499\times10^{-6}}\times(27+273)$

$T_{2}=776\ K$

$T_{2}=776-273=503\ ^{\circ}C$

Hence, The final temperature is 503°C.