Which Container is Hotter After 30s? Exploring Heat Transfer

[LiamNi]

Homework Statement

In each of the following, state and explain which container will have the hotter liquid after thirty seconds:
a) You pour equal amounts of of hot coffee into two cup s from a percolator. The cups are the same general size and shape. One is made from heavy china one is made from delicate china.
b) Your pour equal amounts of hot olive oil into two urns. The urns are the same general size and shape. One is made from pewter the other from brass.
2. The attempt at a solution
The solution is a attached but I still fail to understand. From what I can grasp the rate at which heat is transferred in the the thermal conductivity. However in their answers they talk about specific heat. I fail to understand why the loss of heat from the liquids are not constant.

 

[drvrm]

The solution is a attached but I still fail to understand. From what I can grasp the rate at which heat is transferred in the the thermal conductivity. However in their answers they talk about specific heat. I fail to understand why the loss of heat from the liquids are not constant.

Heat moves more readily in some materials than in others. Metals are good conductors and heat moves readily through them.

Rate of flow of heat by conduction = - k .A . Change in temperature per unit cross section

where A is the area of the cross-section and
k is a constant called the coefficient of thermal conductivity .

The negative sign is there as the temperature gradient is negative

if you see table of k for different materials you will find that brass is a good conductor than the Pewter which is a malleable metal alloy, (traditionally 85–99% tin, with the remainder consisting of copper, antimony, bismuth and sometimes, less commonly today, lead..)

One is made from heavy china one is made from delicate china.

delicate china conducts the heat faster than heavy china so it will be cooled faster.

 

[LiamNi]

That is similar to the understanding I had however the answers in the book do not talk about conductivity and rather answer in terms of specific heat, is there anyway to explain it using that.

Also is there reasoning behind delicate china heating faster than heavy china?

Thanks for your help!

 

[drvrm]

Also is there reasoning behind delicate china heating faster than heavy china?

this effect is basically due to thickness -delicate china approx. is one fourth or even less thick than the thickness of heavy china so the outside convection cooling and transfer of heat is faster through conduction .

That is similar to the understanding I had however the answers in the book do not talk about conductivity and rather answer in terms of specific heat, is there anyway to explain it using that...your quote.

regarding specific heat effects- if you keep some liquid having higher specific heat then
the heat content per degree temperature will be higher
so if identical cooling due to conduction is available to two liquids having lower and higher specific heats -
the liquid having higher sp. heat will be cooling slower as larger amount of heat energy has to be transported .

regarding two different containers having different specific heats of their material -
as the temperature change will be dependent on specific heat the larger specific heat container will show less temp. rise compared to surrounding after conduction through its thickness-
therefore the effective cooling will be less as outside the container Newton's law of cooling will operate and it is proportional to difference in temp. of container and temp. of surrounding.
therefore the material having larger heat capacity will keep the liquids more warm for a longer period.

 

[LiamNi]

In no way am i doubting you are correct however the answers state the opposite. They say the higher specific heat means it will take more heat away.

 

[drvrm]

They say the higher specific heat means it will take more heat away.

well there are three parts of the system -
liquid ; container ; surrounding atmosphere
my arguments were for the cooling of container by the surrounding applying the Newtons law of cooling.
if one focuses on the liquid only
the higher specific heat containers can take larger amount of heat energy due to its specific heat -and the conduction transfer is proportional to difference in temp also ; that will take away more heat energy
and they are correct - the liquid will be cooled more in higher specific heat material/containers.
i revise my arguments but stand on the ultimate cooling of the system of liquid+container.

 

[LiamNi]

OK great thanks for all your help!

 

[LiamNi]

One quick thing to confirm. In the china example is the water no cooling at the same rate since the conductivity is the same. I mean after a longer period of time it may change but initially isn't the energy transfer the same.

 

[drvrm]

One quick thing to confirm. In the china example is the water no cooling at the same rate since the conductivity is the same. I mean after a longer period of time it may change but initially isn't the energy transfer the same.

in the case of china cups/ceramics cups ,the delicate one will have lower temp than the heavy ones as for thickness of the material the heat has to cross-though they are made of low conductivity materials. but one should make a check to confirm.