Thermal Conductivity Ranking Task

[sososo]

Hi :)

I'm having difficulty with finding the relationship between specific heat, c, and thermal conductivity, k and cannot answer these questions -

Six objects are placed in a 500 F (260 C) oven and allowed to reach thermal equilibrium. Each object has a mass of 1.0 kg . The specific heat and thermal conductivity of each substance are denoted by c and k.

Rank these objects on the basis of their temperatures when removed from the oven.
Rank from largest to smallest. To rank items as equivalent, overlap them.

Steak
c: 3500 J /(kgC)
k: 0.2 J /(smC)

Wood
c: 1700 J /(kgC)
k: 0.1 J /(smC)

Aluminium
c: 900 J /(kgC)
k: 220 J /(smC)

Glass
c: 837 J /(kgC)
k: 0.8 J /(smC)

Silver
c: 235 J /(kgC)
k: 420 J /(smC)

Iron
c: 448 J /(kgC)
k: 80 J /(smC)

And also Question 2.

Each of the objects is immediately dunked in an identical tub of cold water. The tubs are quickly sealed and insulated. Rank the objects on the basis of their temperature on reaching equilibrium with the water.

Rank from largest to smallest. To rank items as equivalent, overlap them.

with the same objects.

 

[Mapes]

Hi sososo, welcome to PF. For homework-type questions, we ask that you show your reasoning. Considering what you know about "thermal equilibrium," what is happening in part 1? What processes do specific heat and thermal conductivity involve, and how does this compare to the process in part 2?

 

[sososo]

Well when 2 objects are in thermal equilibrium, no energy flows from one to the other. So for part 1, do i not have to consider thermal conductivity to arrange the objects?

If so, would the arrangement be (from largest to smallest)

Steak
c: 3500 J /(kgC)
k: 0.2 J /(smC)

Wood
c: 1700 J /(kgC)
k: 0.1 J /(smC)

Aluminium
c: 900 J /(kgC)
k: 220 J /(smC)

Glass
c: 837 J /(kgC)
k: 0.8 J /(smC)

Iron
c: 448 J /(kgC)
k: 80 J /(smC)

Silver
c: 235 J /(kgC)
k: 420 J /(smC)


For Part 2

Heat capacity = mass * specific heat (Tf - Ti)
Q = mc(Tf-Ti)

Thermal conductivity = (distance between two ends * heat capacity) / (Cross sectional area of the object * (T1-T2) * t
k = lQ / A(T2-T1)t

I'm not sure where to go from here :(

 

[sososo]

Also by dividing c by k

c: J/kg*C
k: J/s*m*C

c/k = J/kg*C x s*m*C/J = s*m/kg

but I'm not sure what this means / if it's related to the question :( :(

 

[Mapes]

Well when 2 objects are in thermal equilibrium, no energy flows from one to the other.

Going further, what can you say about the temperature of an object in thermal equilibrium with a 500F oven?

Heat capacity = mass * specific heat (Tf - Ti)

This isn't the heat capacity but rather the energy transferred due to a change in temperature. But how, in words, would you describe the processes? Does one describe heat transfer within an object and the other describe heat transfer to or from the external environment, for example?

 

[sososo]

Going further, what can you say about the temperature of an object in thermal equilibrium with a 500F oven?

the object would reach the same temperature as the oven and reaching thermal equilibrium means that it wouldn't lose or gain energy (heat)?

but the temperature of each object should vary because of c shouldn't it?

This isn't the heat capacity but rather the energy transferred due to a change in temperature. But how, in words, would you describe the processes? Does one describe heat transfer within an object and the other describe heat transfer to or from the external environment, for example?

I'm not sure about this one. This is what is confusing me

 

[sososo]

the oven has a fixed temperature so if its in thermal equilibrium with the other objects, the objects would have to increase their temperatures to get in thermal equilibrium with the oven.

the other objects would have a limit to the highest temperature... if it gets too high wood will burn / iron will melt

the limit is related to c and k ?

I'm really confused :( how are c and k related??

 

[Mapes]

the object would reach the same temperature as the oven and reaching thermal equilibrium means that it wouldn't lose or gain energy (heat)?

Agreed.

but the temperature of each object should vary because of c shouldn't it?

Why?

 

[sososo]

the specific heat is the amount of energy required for 1kg to reach 1 C

thermal conductivity is rate of heat conduction?

 

[sososo]

since specific heat is the amount of energy required for 1 kg to reach 1C

so e.g.

for Steak
c: 3500 J /(kgC) = the energy required to get to 1C

so to get to 260 C it would require the steak 910000 J/(kgC) ??

am i going in the right direction?

 

[Mapes]

the specific heat is the amount of energy required for 1kg to reach 1 C

To increase temperature 1 C.

 

[sososo]

okay, so to increase to 1 C eg. for steak...it requires 3500 J /(kgC) of energy?

so to reach 260 C ? would I multiply c by 260 ?

 

[Mapes]

okay, so to increase to 1 C eg. for steak...it requires 3500 J /(kgC) of energy?

so to reach 260 C ? would I multiply c by 260 ?

If you're starting from 0 C.

 

[sososo]

oh my goodness :( I am still very confused.

 

[Mapes]

If you don't have any good reference material or a textbook handy, you might try at least checking Wikipedia for an overview of thermal conductivity and specific heat. There's one thing that the thermal conductivity article doesn't make clear immediately, but that I would emphasize: thermal conductivity governs the rate of heat transfer when temperature differences exist in a system. However, note that both of your problem parts specify that the systems are at thermal equilibrium. In other words, no temperature differences exist. I would also encourage you to visualize the physical system: if you put two materials in an oven and wait a long time (so that they come to thermal equilibrium), then check their temperature, is it a function of either their specific heat or thermal conductivity, or is it a function of the oven temperature only?

 

[sososo]

thank you sooo much!

 

[srikanthdeenu]

Agreed.



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