Any physicists here that can answer this question?

I would take 15 sec.

Engineer spotted, amirite?

ECKS
DEE

well if the cup is of infinite size then the answer is trivially never, but it depends on how big the cup is.

This assumes that the heat capacity is constant u fucking mong.
>For t -> infinity
DUDE LMAO THE ANSWER IS INFINITE

Hence the reason I didn't write anything
>another thread revealing Veeky Forums has little to do with science.
Ecks dee my simple solution that no one else bothered writing else gives me E-ego boost.

15 seconds as rough estimate. Since the convective heat transfer is way more efficient you can pretty much ignore the conduction. There is only one characteristic convective time, 10 seconds, so the answer probably is somewhere between 10 and 20 seconds.

What the fuck is CDD water?
What is the value of a single cupper?

This thing is stupid.

Every number you need is on there

Wrong

Wrong

>is there cold water leaving the cup at a certain rate?
That's what you're supposed to calculate dipshit

Why would you assume it "perfectly displaces" the cold water? What universe do you live in?

Go to your sink and tell us how accurate your "solution" is

>if the cup is of infinite size
It says 1 cup on the cup. Are you illiterate? Why would a physics problem have an "infinitely sized" cup, something that isn't possible in the world of physics?

I think the cup is a cup dude.
1 cup = 8 fl. oz. = 250 ml

No, it says there's a cup of cold water. There's no data on the size of the cup.

It tells you how much cold water is there, I'm perfectly fucking aware that a cup is a unit of volume, but the problem did not state "the container holding the water is full" or the volume of the container explicitly.

If it's not infinite and you're putting hot water in it then it will fill up, you retarded fucking nigger chimp.

I'm aware of that, but the differential equation of the mixing problem would have a piecewise solution in that case, and the answer would be different.

>Go to your sink and tell us how accurate your "solution" is

OK, I just did. I took approximately 15 seconds.

None of this matters if we don't know what material the cup is made of. What if it's some super heat resistant shit or just a thin piece of plastic?

Not relevant

Solving this perfectly involves solving Navier-Stokes

Differential equation for task: [math]\frac{dQ}{dt}=a+bQ[/math].

The answer is something exponential so it takes infinitely time.

Question should be "how long before the difference is nominal?".

This, wouldn't the temperature just approach a limit, but never reach it?

Technically yes.

You have an open system varying constantly: the same flow [math]F \,=\, \frac{\mathrm dm}{\mathrm dt}[/math] of hot water enters the glass as that of water that leaves the glass.

Apply the first law of thermodynamics:
[eqn]\frac{\mathrm dU}{\mathrm dt} \left( t \right) \,+\, F\, \left( h_c \left( t \right) \,-\, h_h \right) \,=\, \frac{\mathrm dQ}{\mathrm dt} \left( t \right) \,+\, \frac{\mathrm dW}{\mathrm dt} \left( t \right)[/eqn]

where [math]U[/math] is the internal energy of the glass, [math]h_c[/math] is the mass enthalpy of the cold water exiting the glass (that is being warmed up), [math]h_h[/math] is the (constant) mass enthalpy of the hot water, [math]Q[/math] is the heat given to the glass and [math]W[/math] is the work done to the glass.

For water, you have [math]\frac{\mathrm dU}{\mathrm dt} \left( t \right) \,=\, \mu\,V\,c\, \frac{\mathrm dT_c}{\mathrm dt} \left( t \right)[/math] where [math]\mu \,=\, 1.0 \,\times\, 10^3 \;\mahtrm{kg \,\cdot\, m^{-3}}[/math] is the volumic mass of water, [math]c[/math] its massic thermal capacity, [math]V[/math] the volume of the glass and [math]T_c[/math] the temperature of the glass. Then, [math]h_c \left( t \right) \,=\, h_h \,+\, c\, \left( T_c \left( t \right) \,-\, T_h \right)[/math] where [math]T_h[/math] is the constant temperature of hot water. We have then
[eqn]\mu\,V\,c\, \frac{\mathrm dT_c}{\mathrm dt} \left( t \right) \,+\, F\,c\, \left( T_c \left( t \right) \,-\, T_h \right) \,=\, \frac{\mathrm dQ}{\mathrm dt} \left( t \right) \,+\, \frac{\mathrm dW}{\mathrm dt} \left( t \right).[/eqn]

Given the height [math]d[/math] between the tap and the glass and [math]g \,=\, 9.81 \;\mathrm{m \,\cdot\, s^{-2}}[/math] the gravitational acceleration, we have [math]\frac{\mathrm dW}{\mathrm dt} \left( t \right) \,=\, F\,g\,d[/math].

I can't workout [math]Q[/math] for convection transfer because I'm just a computer scientist. If anyone here actually did thermodynamics, he may finish my work nobody cares about.

The temperature inside cup is [math]T=(T_0-T_h)e^{-t/10}+T_h[/math] where 0 indicates initial temp and h tap's hot water temp. As predicted, it takes infinitely of time to get the cup as hot as the tapwater unless the initial temp is the same but it's the trivial solution.

OP here. I work on the thermal management team of a large auto manufacturer. This is the question we ask interns during their interview. Not a single one of you would get a position. If you actually start talking about infinite anything you are spending way too much time in remedial books and not thinking about the real world. It's a cup of water, if you manage to turn it into a sprawling equation or start asking about the material of the counter it's on you are never going to be able to accomplish anything in a work environment.

If that were true you would have given us a screenshot of a nicely formatted document instead of a toddler's MS Paint garbage.

10 seconds to displace the water, 10 more seconds to fully fill the cup.

So uh am I right? You are asking about the water in the cup right? Because if you mean the physical cup itself then fuck you lol

There is no document. We ask the question. What do you think, it's a test and they have to show their work? Have you never been outside of a school environment? Many interviewees were able to come up with a great solution without thinking more than a minute, no paper and certainly no calculator needed. That should give you a clue.

How would 100% of the water be displaced instantly? Use common sense ffs.

You could apply that same logic to a car tank running out of fuel. There are infinite decimal places. The engine therefore never runs out of fuel, because there's always one more infinitely small fraction of fuel left.

So being a professional automobile engineer is saying "between 5 and 10 seconds"?

Mechanical, electrical, telecom and computer engineering are the only non-memer branches of engineering after all.

mass of the cup
heat of energy of the cup

volume of the water ---> mass of the water
heat of energy of said water

calculate 1:1 how they'd easily permeate assuming its in a vacuum until they equilibrate

What are you talking about? What is an "automobile engineer"? There are hundreds of systems in modern automobiles. People experienced in their respective systems work in areas related to their field. You very obviously are not any kind of engineer, nor are you likely to ever be one with the kind of intelligence you are displaying.

yes the heat capacity of the cup should be constant throughout the mass of the cup. Same with the water

>What is an "automobile engineer"?
My bad, I meant "thermomonkey working for the automotive industry". Not that you understood me well and didn't just wanted to sperg me out and show how pathetic your life is.

How could I understand you? Not only is your mastery of English poor, you tried to make a post insinuating that such a thing as an "automobile engineer" exists, and that they are inferior to mechanical, electrical, and computer engineers somehow, while in reality automotive companies employ people in those fields, including me.

It would not be instant. It would take 10 seconds.

The answer is less than or equal to 20 seconds.

Bump

wouldn't you need at least the heat capacity of the cup? or its density for that matter to calculate the mass so that you can use Q=mcT and then put it in S=dQ/dt and solve for dT?

or am i thinking about the the wrong way?

You just said everyone was wrong and didn't offer any simulacrum of concrete solutions yourself.

The hot water would displace mixed water at a constant rate, and the mixture will always become more and more "hot," but since you started with cold water, it'll become half cold, then a quarter cold, then an eighth cold, and so on, ad infinitum. That's an exponential distribution of hot water in the cup, meaning it will never reach the hot water temperature, and you would know that if you ever opened a book on differential equations, control theory, or fluid mechanics.

If you want to be pedantic, the water in the cup will constantly lose heat due to radiation and convection with the air around it, meaning it still never reaches the hot water temperature. If you want to be really pedantic about the question, the cup itself will follow a temperature distribution wherein it's the temperature of the mixed water on both the inside and outside but never the temperature of the hot water itself because that mixed water follows an exponential temperature profile over time. Either way, the answer is infinity.

What's your solution?

Wont the cup just break anyway?

In an interview context, the answer is to ask more questions about the problem. How accurate do we need our answer to be? If we just need a qualitative guess, we can put it at 30 seconds, just to have a factor of safety in there. Make it longer if we need a high factor of safety. If we need actual data, it's quicker to run tests than numbers on something simple like this, so the answer is to "run tests."

If he asks what kind of tests, the test is to get a cup full of cold water with a thermometer in it, get another cup to measure out a faucet rate of 1/10th of a cup of hot water per second, put a thermometer in the hot water cup to find the temperature of the hot water, then start a stopwatch when you put the cold water with the thermometer underneath that hot faucet. When the cold water thermometer just about matches the hot one, stop the timer. Do this a few times, and you'll have not only an approximate answer but also data to back it up and a pretty cheap test to confirm the results.

In the context of Veeky Forums, you should know better. Numbers, equations, calculators, textbooks, and Google. Context matters.

if you're really the op, it seems really fucking important for you to mention that you want us to imagine that we're asked this in an interview

Here I have plotted the solution [math]T=(T_0-T_h) e^{-t/10}+T_h[/math],

with conditions
[math]T_h=50^\circ \text{C}=323.15 \text{K}[/math] and
[math]T_0=0^\circ \text{C}=273.15\text{K}[/math].

It takes nearly a minute to get near to tap water temp. It will never be as hot but after a minute it should suffice.

You guys have nothing better to do?

My girlfriend comes over after tomorrow. So, until then: no. After that, it's sexy time.

If you mean the exact same, never. Depending on your definition of "close enough" we can work something out.

Fuck off Zeno

>implying Veeky Forums can't solve NS

WOW. Someone finally got the job. Congrats user, you might make it in this field.

The correct answer is "do you have a cup and a thermometer." It's obviously a complete waste of time to try to model this in an equation. Now go try it thread, maybe you'll learn something. Here's a hint, it's not anywhere close to 10 seconds.

this contribution must've been exhausting for you.
>you're wrong
>all solutions are wrong
>watch me offer nothing to prove it wrong
>and scream "wrong" over and over again
>trust me its all wrong

>Why would a physics problem have an "infinitely sized" cup, something that isn't possible in the world of physics?
you are new to physics right?

>Many interviewees were able to come up with a great solution without thinking more than a minute, no paper and certainly no calculator needed.
>That should give you a clue as to the answer I still refuse to provide ITT.
The solution is so simple yet you can't tell us what it is because you don't know it either you dumb arrogant cunt.

>The correct answer is "do you have a cup and a thermometer." It's obviously a complete waste of time to try to model this in an equation. Now go try it thread, maybe you'll learn something. Here's a hint, it's not anywhere close to 10 seconds.
lel you hire brainlets

>>[math]T=(T_0-T_h) e^{-t/10}+T_h[/math]
why?

to elaborate:
for T(t) to be T(t) = c*exp(m*t) you would need a ODE of the form dT/dt = m*T. Now i dont see how this could be the case as T = d * Q for some d.
Then you get dT/dt = d*dQ/dt = m*d*Q.
But the rate of change of the thermal energy is constant and independend of the current amount of the thermal energy of the cup. at least how i understand the problem.

Clearly it satisfy the initial condition [math]T=T_0[/math]

Differentiate respect to time to get
[math]-10 \frac{dT}{dt}=(T_0-T_h)e^{-t/10}[/math]

But this is just
[math]-10 \frac{dT}{dt}=T-Th[/math]
or [math]\frac{dT}{dt}=Th/10 -T/10[/math]
multiply by spesific heat capasity and density of water to get
[math]\frac{dQ}{dt}=\dot{Q}_{in}-\dot{Q}_{out}[/math]

the mistake is the line

[math] \frac{\delta T}\{\delta t} = \frac{T*h}{10} - \frac{T}{10} [/math]

on the left side you ahve the temperature of the water within the cup. on the right side you have what? The first T on the right hand side has to mean the temperature of the water pouring in. And that is constant.

Here is my work

ah i see you consider the water spilling out. that solves the contradictory results.
thank you :)

I could be completely wrong, but I feel like it won't be the same every time.

The hot water hitting the cold water will be a chaotic system, so we can't predict how much of the water overflowing out of the cup will be cold water or hot water.

>heat of the cup

There is no such thing as "heat of the cup", heat isn't a state function. What you mean is internal energy.

You can assume mixing, which is a valid assumption to a good approximation.

I think he meant water equivalent

Um... no.

An engine uses O(1) amount of fuel each ignition cycle. If the engine was using a certain fraction of the fuel each cycle, your analogy would have been sound, but it's not. So kill yourself, thx.

just did it faggot. 15 seconds.

i appreciate your post, user

wrong

This guy gets it. Infinite amount of time

Assuming either
1. the cup is not affected by the temperature of the surrounding air
2. the temperature of air is less than or equal to the temperature of the hot water

This guy is right too

Also this is a stupid question. We are given such a small amount of information there are really only two possibilities (assuming there is a solution):

10 seconds
or infinite amount of time

Anyone with problem solving skills could narrow it down to this.

Then, if you have basic knowledge about heat transfer or have ever played with your sink you'd know it was obviously not 10 seconds.

Well the how water will "mix" with the cold water. Part of this "mix" will fuck off due to overflow. However regardless it still gives heat energy to the cup so it will get hotter and hotter.

If I would have to guess it's an exponential curve something like newton's law of cooling so it will probably get near in 50 seconds.

I forgot to add; you can just measure it if you are allowed to it experimentally. You can adjust the valve, measure times, etc and make some nice plots, but where is the fun in that?

/Thread

Attempt suicide my friend

It's a physics question not an engineering question. It never reaches the hot water temperature. It gets close, but never quite there.

So what is the mistake?