How to measure the time for temperature drop?

[beansbaxter]

I have to change the oil on my motorcycle, trouble is that I like to warm up the oil before I change it. Unfortunately if the oil is too hot it might burn me so I like to let it cool down for a while before I change it.

If my bike runs at 80 C when it is fully warmed up on a 25 C day and I want to change the oil when it gets to 40 C, how long do I have to wait before I can change the oil if after 15 minutes the temp drops by 5 C?

Assuming that the day stays at a consistent 25 C while I am waiting.

 

[f95toli]

This sounds like homework. Try using Newton's law of cooling.

 

[BrownTown]

you cant really determine that since you don't know enough about the proportionality constant in order to determine the rate of cooling. I'd say just touch it and see if its hot?

 

[f95toli]

Originally posted by: BrownTown
you cant really determine that since you don't know enough about the proportionality constant in order to determine the rate of cooling. I'd say just touch it and see if its hot?

Yes, you can. If you know that at time t=0 the temperature is 80 degrees C and t=15 min the temperature is 75 degrees C, then you can easilty calculate the constant.

 

[bobsmith1492]

This is a problem straight out of dif-eq. class... or maybe even earlier. (?)

 

[gsellis]

I thought I remember this being an inverse log function. The percentage of decrease decreases over time. Been 25 years since I cared 😉 .

 

[BrownTown]

Originally posted by: f95toli

Originally posted by: BrownTown
you cant really determine that since you don't know enough about the proportionality constant in order to determine the rate of cooling. I'd say just touch it and see if its hot?

Yes, you can. If you know that at time t=0 the temperature is 80 degrees C and t=15 min the temperature is 75 degrees C, then you can easilty calculate the constant.

Yeah, but if you can measure the temperature than you don't need to use the equation in the first place becasue you can just wait till your thermometer reads the temperature you want to start at. We are assuming he can't do that or there would be no question here.

 

[bobsmith1492]

Originally posted by: BrownTown

Originally posted by: f95toli

Originally posted by: BrownTown
you cant really determine that since you don't know enough about the proportionality constant in order to determine the rate of cooling. I'd say just touch it and see if its hot?

Yes, you can. If you know that at time t=0 the temperature is 80 degrees C and t=15 min the temperature is 75 degrees C, then you can easilty calculate the constant.

Yeah, but if you can measure the temperature than you don't need to use the equation in the first place becasue you can just wait till your thermometer reads the temperature you want to start at. We are assuming he can't do that or there would be no question here.

Hm, that's true... makes it sound like a HW question to me.

Solution: Watch the thermometer until it hits 40C. 🙂

 

[dkozloski]

It's got to be a homework question. No dyed in the wool motorcycle owner would worry for an instant about being burned during an oil change of his beloved machine.

 

[PlasmaBomb]

The answer is that if the oil runs at 80*C when its warm you take out the sump plug when you turn the engine off. It's always better to change it when its warm and less viscous.

 

[f95toli]

Originally posted by: BrownTown

Originally posted by: f95toli

Originally posted by: BrownTown
you cant really determine that since you don't know enough about the proportionality constant in order to determine the rate of cooling. I'd say just touch it and see if its hot?

Yes, you can. If you know that at time t=0 the temperature is 80 degrees C and t=15 min the temperature is 75 degrees C, then you can easilty calculate the constant.

Yeah, but if you can measure the temperature than you don't need to use the equation in the first place becasue you can just wait till your thermometer reads the temperature you want to start at. We are assuming he can't do that or there would be no question here.

That is why this sounded like homework to me: The required information WAS in the question.
That said, there IS a point to this; since the drop is exponential it might take quite a while but if you measuret the temperature after 5 minutes it will give you enough information to to figure out HOW long and then you can leave and do something better (have a pint) while you wait.
I actually do this from time to time; in my case the time might be between 2 and 6 hours so it makes sense to try to calculate it and then leave and come back later instead of staring at thermometer for maybe 6 hours.

 

[Born2bwire]

Originally posted by: f95toli

Originally posted by: BrownTown

Originally posted by: f95toli

Originally posted by: BrownTown
you cant really determine that since you don't know enough about the proportionality constant in order to determine the rate of cooling. I'd say just touch it and see if its hot?

Yes, you can. If you know that at time t=0 the temperature is 80 degrees C and t=15 min the temperature is 75 degrees C, then you can easilty calculate the constant.

Yeah, but if you can measure the temperature than you don't need to use the equation in the first place becasue you can just wait till your thermometer reads the temperature you want to start at. We are assuming he can't do that or there would be no question here.

That is why this sounded like homework to me: The required information WAS in the question.
That said, there IS a point to this; since the drop is exponential it might take quite a while but if you measuret the temperature after 5 minutes it will give you enough information to to figure out HOW long and then you can leave and do something better (have a pint) while you wait.
I actually do this from time to time; in my case the time might be between 2 and 6 hours so it makes sense to try to calculate it and then leave and come back later instead of staring at thermometer for maybe 6 hours.

Yeah, if he's able to measure the temperature, then he can just let it sit and check on it periodically until it's the temperature he wants. Then write down how long it took.

 

[DrPizza]

Originally posted by: bobsmith1492
This is a problem straight out of dif-eq. class... or maybe even earlier. (?)

A similar problem is in the pre-calculus text in the log/exp functions chapter. Newton's law of cooling is covered in a half dozen problems in the calculus text I use. (And, I'm sure it's in diff eq's texts as well.)

Oh, and for the OP: The correct answer is to not let the bike warm up to 80C. Only warm it up until it reaches 40C. That way you save gas and time. 😛 🙂

 

[beansbaxter]

This was never a homework question by the way. I dont know why everyone always assumes every question asked is homework. I graduated college in 2002 and havent looked back since. Anyways...

This really was for real world use. It's not that I dont mind changing the oil on my motorcycle when it's hot, but I wanted to sincerely figure out how long it took in time to measure temperature drop. There is more to it than that.

As an example, I noticed my temp would drop 10 degrees in 5 minutes. If I wanted it to drop another 30 degrees, it would not take another 15 minutes because it cools off faster. There is exponential decay happening, if that is the right term.

The Newton law of cooling seemed to answer my question, thanks.