Calculating the Final Temp of an XK8 Cylinder Using the Ideal Gas Law

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To calculate the final temperature of a Jaguar XK8 cylinder using the ideal gas law, the initial conditions include a volume of 499 cm³, atmospheric pressure of 1.01×10^5 Pa, and a temperature of 27.0°C. The compression results in a final volume of 46.2 cm³ and a gauge pressure of 2.72×10^6 Pa, leading to a final absolute pressure of 2.821×10^6 Pa. The ideal gas law formula (p1v1/T1 = p2v2/T2) is applied, but it is crucial to convert temperatures to Kelvin for accurate calculations. A common mistake noted was the failure to convert the initial temperature to Kelvin, which affects the final result. Correctly applying the ideal gas law with proper conversions will yield the accurate final temperature.
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A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499cm^3 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 cm^3 and the gauge pressure has increased to 2.72×106 Pa. Compute the final temperature.

I ended up with 69.8 degrees. I used the ideal gas law, but because the mass of air remains constant, i used:

(p1v1/T1) = (p2v2/T2)

I converted the volume to 4.99 x 10^-4 and 4.62 x 10^-5. I also dtermined the final absolute pressure, which is 2.821 x 10^6. But my answer is wrong. Could someone please help.
 
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It's ok...i forgot to convert to Kelvin.
 
Classical mistake.The weird part is that u converted the volume...:eek:

Daniel.
 
Use the ratios of the volumes, so as dex said you don't need to convert. Also, as you understood, always work with Kelvin!
 
I hope u see that u need the conversion to K in both the initial & final temperature...

Daniel.
 
How did you find the final absolute pressure?
 

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