When the temperature of an automobile tire is 20^∘ C, the pressure in the tire reads 32 psi on a

When the temperature of an automobile tire is 20^∘ C, the...

Key Concepts

Constant Volume Processes

In a constant volume process, the volume of the system remains unchanged, which implies that any change in temperature directly affects the pressure. This characteristic is described by Gay-Lussac's law, a special case of the ideal gas law, and is key to understanding how temperature variations influence gas pressure in closed systems.

Gauge Pressure vs Absolute Pressure

Gauge pressure is the pressure measured relative to the ambient atmospheric pressure, whereas absolute pressure is the total pressure including atmospheric pressure. When working with the ideal gas law, it is essential to use absolute pressures to accurately describe the physical state of the gas.

Ideal Gas Law

The ideal gas law relates pressure, volume, temperature, and the number of moles of a gas through the equation PV = nRT. It provides a useful approximation for the behavior of gases under many conditions, especially when dealing with processes at constant volume where pressure and temperature changes are directly proportional.

Temperature Conversion

Temperature must always be converted to an absolute scale, such as Kelvin, when using the ideal gas law. This is because the Kelvin scale starts at absolute zero, ensuring that ratios and proportional changes in temperature are physically meaningful when applied to equations involving thermal processes.

Transcript

00:01 Okay, so in this problem, we are looking for the pressure of a tire when it heats up to 40 degrees.

00:09 So let's get down the givens and we can discuss how to do the problem.

00:12 So it's final temperature, it's 40 degrees c, and i want to immediately convert this to kelvin if i'm going to use the ideal gas law.

00:21 I think it's generally a bad idea to use celsius in the ideal gas law because the relationship between these is additive.

00:27 So you're never going to do any unit cancellations like you would be if it were multiplicative.

00:33 And if that's hard to understand, i mean, just try to just do a problem with celsius and see how it goes wrong.

00:41 Or maybe it won't.

00:43 Maybe there's something i'm missing, but some edge case.

00:47 But anyway, so, okay, so 273 plus 40 is 313 kelvin.

00:59 And the initial temperature is 20 degrees celsius.

01:08 And so again, let's convert that to kelvin.

01:12 So then we get 293 kelvin.

01:17 I think if you're doing temperature differences, it's okay to not convert.

01:20 I think that was the case that i had in the back of my mind.

01:23 Okay.

01:25 And psi, the pressure is 32 psi.

01:28 Here, p initial 32 psi.

01:33 And then our goal is to get, i think, the pressure, the final pressure.

01:48 So let's use the ideal gas law.

01:50 We know for the error in there, pv is equal to nrt.

01:58 And let's say if r and t and n stay the same, we know from initial to final, that p initial, v initial, is equal to p final.

02:09 V -final.

02:11 And then let's point out, too, i think that these p's are gauge pressure.

02:14 So that means that the total, and we want to use absolute pressure here.

02:22 So actually the absolute pressure, sort of like we did with temperature, we need to add the 14 psi from the atmosphere.

02:32 Because, i mean, air already produces, you know, produces pressure.

02:38 And so this is the additional pressure you need or else the tire would be.

02:41 Be deflated.

02:43 So then the initial total pressure is actually 46 psi...

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