Question

A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499cm3499cm 3 of air at atmospheric pressure (1.01×105Pa)(1.01×10 5 Pa) and a temperature of 27.0∘C27.0 ∘C. At the end of the stroke, the air has been compressed to a volume of 46.2cm 346.2cm 3 and the gauge pressure has increased to 2.72×106Pa2.72×10 6Pa. Compute the final temperature.

Answer 1

Answer:

503°C

Explanation:

According to the given situation, the computation of the final temperature is shown below:

In this question we use the law of ideal gas i.e

pV = nRT

i.e

$\frac{p_1V_1}{T_1} = \frac{p_2V_2}{T_2}$

Therefore

$T_2 = T_1 (\frac{p_2}{p_1}) (\frac{V_2}{V_1})$

$= 300\ k (\frac{2.72 \times 10^{6} Pa + 1.01 \times 10^{5} Pa}{1.01 \times 10^{5} Pa})(\frac{46.2 cm^3}{499 cm^3})$

= 776 k

= (776  - 273)° C

= 503°C

Therefore the final temperature is 503°C

We simply applied the above formulas so that the final temperature could arrive