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A car tyre gauge reads 220 kPa early on a cold morning, at 12 °C…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A car tyre gauge reads kPa early on a cold morning, at . The air outside is at kPa. After a long drive the air in the tyre is at . Take the volume of the tyre as fixed. What is the absolute pressure in the tyre then, and what does the gauge read?
Need a reminder? The key ideaShow
For an ideal gas, with in kelvin and the absolute pressure:
For a fixed amount of gas, . The density of a gas is .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. Gauge kPa, outside kPa, K, K.
Step 1. Absolute pressure at the start. kPa.
Step 2. The pressure law. We want , so kPa.
Step 3. The gauge. kPa.
Answer: kPa absolute; the gauge reads kPa.
Watch out. Using the gauge reading in the law gives kPa, which is wrong. Using degrees Celsius would give a rise of almost four times, which is far too much.
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