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

503°C

Step-by-step 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

`(p_1V_1)/(T_1) = (p_2V_2)/(T_2)`

Therefore

`T_2 = T_1 ((p_2)/(p_1)) ((V_2)/(V_1))`

`= 300\ k ((2.72 * 10^(6) Pa + 1.01 * 10^(5) Pa)/(1.01 * 10^(5) Pa))((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