Logic, IQ, and Lateral Thinking Problems.

[ET, the Extra Terrestrial]

E wuz a feller wif a pertickler odd shaypt pryvit parte, iffen ye nose wat Oi meenz... E were feet shored inn sevrull o Black Barrght's pro duck shunz halong sighed sech know ta bulls as Big Bertha hand Large Marge. Large Marge sed she thot she reely got scrood on the deel.

[Mad Willyum Bonney]

Rev , ye durdy chettar ! Oi luvs ye ! No moor prises fur ye tho !

Roy , nope , no see gar fur ye !

Hokay ET ! Ye wins thee chess full ove wee iddy biddy grog glasses . Ye noes thee drill.

[Roy Hunter]

Gone kind-of quiet since the prize incentive disappeared...

You make two cups of tea. Both cups are exactly the same size, made of the same material, sitting the same environment (a kitchen at room temperature); you use exactly the same amount of boiling water from the same kettle, so we can assume all things are equal so far.

You take the milk out of the fridge, and add an amount of cold milk to one cup. You return the milk to the fridge, and leave both cups to stand for 10 minutes. Then you take the milk back out of the fridge and add exactly the same amount of cold milk to the other cup.

You now have two cups of tea. Which one is hotter? Why?

[daftbeaker]

The one you added the milk to the second time.

Easy, if you're returning the milk to the fridge then you're not leaving it in the first cup of tea. QED

[DavidH]

But in the end both cups get the same amount of milk added, the milk being at the same temperature both times. I'm no scientist, but it seems to me that the cup with no milk will lose heat faster than the milky one, as the temperature gradient is steeper. Thus, when you add the milk later the mixture will be at a lower temperature.

[daftbeaker]

But in the end both cups get the same amount of milk added, the milk being at the same temperature both times.

But only one cup has milk in it at the end.

The first cup is a dead herring, watch. You have cup of tea and add milk. You now have cup of tea + milk. Then you return the milk to the fridge, leaving you with cup of tea again. Either my devious reading of the question is correct or I'm just very suspicious of these daft riddles

[DavidH]

I reckon you're being too suspicious there, db, though these riddles can be very sneaky. OK, it should really say "returned the remaining milk..."

What's your opinion if it's not a trick question?

[daftbeaker]

I reckon you're being too suspicious there, db, though these riddles can be very sneaky. OK, it should really say "returned the remaining milk..."

What's your opinion if it's not a trick question?

My opinion is 'do the experiment and find out' I know I don't often mention my liking for reality over waffling

Honestly, I don't know. It could be worked out but you'd need to spend a while working out specific heat capacities and rates of cooling. At a guess I'd say the second one, both due to temperature differences as you pointed out and the hotter cup will lose more water by evaporation, meaning the milk will be a greater proportion at the end.

[Roy Hunter]

You cannot remove milk from a cup of tea once you've added it (O'Nine, 2011). You dolt.

The cups are the same. The initial temperature of the water is the same. The volume of water is the same. The amount of milk which is added to each cup is the same, and the milk is at the same temperature when it is added to the tea. Assume all other things are equal: ceteris paribus. The only difference between the two cups of tea is the time when the milk is added.

Which one is hotter?

References
O'Nine, P. (2011), 'How To Mayke a Fyne Cuppe of Tea', Pastafarian Doctoral Theses, (1:13, p555445), doi: viewtopic.php?f=1&t=20941#p555445

[daftbeaker]

You cannot remove milk from a cup of tea once you've added it (O'Nine, 2011). You dolt.

With these devious questions anything is possible.

How do you get an elephant in a fridge?
Open the door and put the elephant in.

How do you get a giraffe in the fridge?
Open the door, take the elephant out and put the giraffe in.

[Roy Hunter]

How do you fit four elephants into a Mini?
Two in the front and two in the back.

How do you know there is an elephant in your fridge?
It's parked the Mini in a 'Giraffe Permit Holders Only' spot in the kitchen.

[PKMKII]

You now have two cups of tea. Which one is hotter? Why?

Wouldn't the one you added the milk to first be hotter? The tea's had time to bring up the temperature of the milk, whereas the second one just had it added. Plus, the cup that didn't have the milk added to it originally is boiling hot, so the evaporation process is going to draw energy out of the surrounding matter. Adding the milk partially arrests that.

[Roy Hunter]

We have a winner!

The cups of tea and the environment are both moving towards the same temperature (thermodynamics, anyone?). The cup of tea (initially) with milk is cooler, and therefore loses less energy to the environment than the cup of tea (initially) without milk. The environment gains more energy from the milkless tea than from the milky tea.

The important bit is that the environment is warming up as the tea cools.

Add the same amount of cold milk to the (initially) milkless tea as you did to the (initially) milky tea, and it ends up colder than the (initially) milky tea because the (initially) milkless tea lost more energy to the environment in the same amount of time than the (initially) milky tea did, and the environment gained more energy from the (initially) milkless tea than it did from the (initially)milky tea.

[pieces o'nine]

May I add that I am proud to have my dissertation cited in a scientific argument. Harrumph.

[Helium Hands]

I'm really glad I missed this discussion.