A few conceptual questions on Heat and Temperature

[iitjee10]

Q1. A thermometer is laid out in direct sunlight. Does it measure the temperature of the air, or of the sun, or of something else?

Q2. Two bodies made of the same material have the same external dimensions and appearance, but one is solid and the other is hollow. When their temperature is increased by the same amount, is the overall volume expansion the same or different. What about the size of the hole of the hollow one? Please explain

I have got some others which I will ask after I get these two understood.

 

[nooma]

Q1. A thermometer is laid out in direct sunlight. Does it measure the temperature of the air, or of the sun, or of something else?

A thermometer measures the temperature by volume taken up by the liquid (formerly mercury). When laid in direct sunlight, I think, there is extra energy being measured by the thermometer due to the UV radiation and light.

Q2. Two bodies made of the same material have the same external dimensions and appearance, but one is solid and the other is hollow. When their temperature is increased by the same amount, is the overall volume expansion the same or different. What about the size of the hole of the hollow one? Please explain

the base answer is that it comes down to the material they are made of as many different materials have different properties.

generally, assuming there is a vacuum in the hollow of the second one, the solid one would be larger. The space taken up by a solid object is determined by the structure of the solid. This increases or decreases a little according to it's temperature. Just think of large metal structures (the Eiffel tower has no specific height as it changes so much due to expansion and contraction of the metal within the structure)

The solid ball has a larger amount of substance to repel therefore any perceptable change would be larger in that one

 

[Doc Al]

generally, assuming there is a vacuum in the hollow of the second one, the solid one would be larger. The space taken up by a solid object is determined by the structure of the solid. This increases or decreases a little according to it's temperature. Just think of large metal structures (the Eiffel tower has no specific height as it changes so much due to expansion and contraction of the metal within the structure)

The solid ball has a larger amount of substance to repel therefore any perceptable change would be larger in that one

Assuming the material is isotropic, all linear dimensions will increase by the same factor, including the hole. Solid or hollow doesn't matter.

 

[nooma]

:S

but the material inside the solid ball will also need to expand, would this not creat a greater overall expansion in the same way that large structures experince large changes due to the change in temperature?

 

[Doc Al]

but the material inside the solid ball will also need to expand, would this not creat a greater overall expansion in the same way that large structures experince large changes due to the change in temperature?

No. Large structures experience large changes due to their size, not because they are solid or hollow. A large hollow ball will expand more than a small solid ball. (Assuming you uniformly increase the temperature by the same amount.)

 

[nooma]

yes... i know that to be true. However they both have the same external measurements. therefore there is a lot more stuff in the solid one that needs to expand.

 

[Doc Al]

therefore there is a lot more stuff in the solid one that needs to expand.

So? Imagine a solid ball. Mentally divide it into a thick shell and a solid core. The thick shell expands just enough to make room for the expanded solid core. (The shell expands the same whether the core is solid or empty.)

 

[nooma]

oh ok... fair enough then.

 

[Mapes]

A hollow object expands exactly as much as a solid object, given that both materials are in a vacuum and the hollow object contains a vacuum. In contrast, a balloon filled with air, for example, would expand much more than a solid sphere of balloon material.

 

[Doc Al]

A hollow object expands exactly as much as a solid object, given that both materials are in a vacuum and the hollow object contains a vacuum. In contrast, a balloon filled with air, for example, would expand much more than a solid sphere of balloon material.

Excellent point.

 

[f95toli]

Q1. A thermometer is laid out in direct sunlight. Does it measure the temperature of the air, or of the sun, or of something else?

It measures the temperature of the thermometer; i.e. what it will show depends on how efficiently it is heated by the sun and cooled by the air, the temperature of any surface it is in contact with etc.

The only time you can trust a thermometer to show the "true" temperature of an object is if the thermometer and object in question are in thermal equilibrium. A thermometer lying in the sun won't tell you anything meaningful.

 

[Cyrus]

Q1. A thermometer is laid out in direct sunlight. Does it measure the temperature of the air, or of the sun, or of something else?

Google how hot the sun is, and see if that seems reasonable to you.

 

[iitjee10]

Thanks a lot everybody.

Now here are a few others
Q3. When water is placed in ice-cube trays in a freezer, why does the water not freeze all at once when the temperature has reached 0 degrees Celsius? In fact the water freezes first in a layer adjacent to the sides of the tray. Why?

Is it because that the heat transfer will take through the surfaces in contact? So when heat is lost it will be done through the layer adjacent to the tray.

 

[nooma]

just to let you know...the energy of the molecules within a substance can be modeled by something called a maxwell-boltzmann curve. its pretty much a bell curve. So at a given temperature the molecules will still have different energy levels. So it will take a while for all to be locked into a rigid lattice of ice.

Now as to why it freezes from the edges in, I would say that the ice cube tray would hold the 'cool' better than the air in the freezer. this means It would be able to cool down the water in the tray more effectively than the air with the surface of the water

 

[bm0p700f]

It freezes at the edge as there more nucleation sites for the ice crystals on the surface of the container than with the body of water.

If there are few nucleation sites i.e smooth container and contamination free water then the water would super cool. this is possible down to about -20 degrees C for water I think.

 

[dx]

Q1. A thermometer is laid out in direct sunlight. Does it measure the temperature of the air, or of the sun, or of something else?

A mercury thermometer for example would measure the temperature of the mercury column. If the column has achieved thermal equilibrium with it's environment, then the temperature of the column and the environment is the same, so it would measure the temperature of the environment. Say you have a gas of some type, and you shine light on it. Eventually, the field of photons and the gas will reach thermal equilibrium*, so by measuring the temperature of the gas you will also be measuring the temperature of the electromagnetic field.

*I don't have the knowledge to work out how long this would take for air and sunlight, but it depends on how strongly the gas and electrodynamic degrees of freedom are coupled. it's also possible that the mercury-electrodynamic coupling is stronger than the gas-electrodynamic coupling, so equilibrium with the light may be achieved faster than with the air (called a partial equilibrium), and in this case it would measure the temperature of the light first.