A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499 cm3cm3 of air at atmospheric pressure (1.01×1051.01×105 PaPa) and a temperature of 27.0∘C∘C. At the end of the stroke, the air has been compressed to a volume of 46.2 cm3cm3 and the gauge pressure has increased to 2.72×1062.72×106 PaPa.

Complete Question

A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499cm3 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 46.2cm3 and the gauge pressure has increased to 2.72×106Pa. Compute the final temperature.

The final temperature is

Explanation:

From the question we are given

       The volume of one of the cylinders is

      The atmospheric pressure is

       The temperature is

       Volume at the end of the stroke is

       The increased pressure  is

Now to obtain the temperature we are going to apply the ideal gas equation to this question and this is mathematically given as

Where P is the pressure , V sis the volume T is the temperature

While is the rate constant and n is the number of mole which is constant in this question  hence

                       =>

Making the subject of the formula we have

 Therefore  

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