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

In summary, a Jaguar XK8 convertible with an eight-cylinder engine has compressed 499cm^3 of air at atmospheric pressure and a temperature of 27.0 C to a volume of 46.2 cm^3 and a gauge pressure of 2.72×106 Pa. Using the ideal gas law and the constant mass of air, the final temperature was calculated to be 69.8 degrees after converting to Kelvin. However, the answer was initially incorrect due to forgetting to convert to Kelvin, which is necessary in both the initial and final temperatures.
  • #1
~angel~
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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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  • #2
It's ok...i forgot to convert to Kelvin.
 
  • #3
Classical mistake.The weird part is that u converted the volume...:eek:

Daniel.
 
  • #4
Use the ratios of the volumes, so as dex said you don't need to convert. Also, as you understood, always work with Kelvin!
 
  • #5
I hope u see that u need the conversion to K in both the initial & final temperature...

Daniel.
 
  • #6
How did you find the final absolute pressure?
 

1. What is the ideal gas law?

The ideal gas law is a formula that describes the relationship between the pressure, volume, temperature, and amount of gas in a system. It is written as PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature.

2. How can the ideal gas law be used to calculate the final temperature of an XK8 cylinder?

To calculate the final temperature of an XK8 cylinder using the ideal gas law, you would need to know the initial pressure, volume, and temperature of the gas inside the cylinder, as well as the amount of gas present. Then, you can rearrange the ideal gas law equation to solve for the final temperature (T2) by dividing both sides by nR and plugging in the known values.

3. What is an XK8 cylinder?

An XK8 cylinder is a type of engine cylinder used in Jaguar XK8 cars. It is a component of the internal combustion engine and is responsible for compressing the fuel-air mixture and igniting it to generate power.

4. Why is the ideal gas law used to calculate the final temperature of an XK8 cylinder?

The ideal gas law is used because it is based on the assumption that the gas inside the cylinder behaves like an ideal gas, meaning that it has no intermolecular forces and its particles have negligible volume. This assumption is valid for most gases at low pressures and high temperatures, making the ideal gas law a useful tool for calculating the final temperature of an XK8 cylinder.

5. What are the units of measurement used in the ideal gas law?

The units of measurement used in the ideal gas law depend on the specific values being input. Pressure is typically measured in pascals (Pa) or atmospheres (atm), volume in cubic meters (m3) or liters (L), temperature in Kelvin (K), and amount of gas in moles (mol). The gas constant (R) can have different units depending on the units used for the other variables, but one commonly used value is 8.314 J/mol*K.

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