Thermodynamics question

[WillJ]

Could someone explain to me how to solve this problem?

A small "coffee cup" calorimeter contains 110 g of H20 at 22.0°C. A 100-g sample of lead is heated to 90.0°C and then placed in the water. The contents of the calorimeter come to a temperature of 23.9°C. What is the specific heat of lead?

I of course could look up the specific heat in a chart, but supposedly you can calculate it from the info given. But I can't figure out how (although I imagine it's incredibly simple and I look like an idiot right now).

While we're at it, a general question that I was wondering: What exactly does temperature measure?

 

[ainwood]

Temperature measures the kinetic energy of molecules.

To solve the equation, Energy = mCp dT, and note that the energy gained by the water will be lost from the lead (assume total energy is conserved). Cp for water is about 4.18 kJ/kgK

 

[Perfection]

You need the specefic heat of water which is 4.186 J/gK

Edit: Ainwood, you meanie

 

[Cuivienen]

Q = mCΔT (Heat = Mass * Specific Heat * Change in Temperature)

The heat lost by the lead is equal to the heat gained by the water. Thus:

m(w)C(w)ΔT(w) = m(Pb)C(Pb)ΔT(Pb)

And solve using the specific heat of water as given to you above.

EDIT: IIRC, Temperature measures the average kinetic energy of the molecules or atoms. Of course, temperature itself isn't given in joules or even a unit of energy.

 

[WillJ]

Temperature measures the kinetic energy of molecules.

I thought the kinetic energy of molecules was heat, measured in joules (or calories), and thus I assumed degrees of temperature must measure something else.

To solve the equation, Energy = mCp dT, and note that the energy gained by the water will be lost from the lead (assume total energy is conserved). Cp for water is about 4.18 kJ/kgK

All right, I actually knew all that; I just wasn't thinking right. So I should:

1. Find out the energy the water gains by

q = m x c x ΔT

or in this case q = 110g x 4.18J/g°C x 1.9°C

2. This is the same amount of energy that the lead loses, thus I can use the same equation, except this time I know q (from the above work) and am looking for c. This time ΔT is 90.0 minus 23.9, or 66.1°C.

Right?

 

[Yom]

I thought the kinetic energy of molecules was heat, measured in joules (or calories), and thus I assumed degrees of temperature must measure something else.All right, I actually knew all that; I just wasn't thinking right. So I should:

1. Find out the energy the water gains by

q = m x c x ΔT

or in this case q = 110g x 4.18J/g°C x 1.9°C

2. This is the same amount of energy that the lead loses, thus I can use the same equation, except this time I know q (from the above work) and am looking for c. This time ΔT is 90.0 minus 23.9, or 66.1°C.

Right?

It all looks right to me, except the units of temperature are in Kelvin, but since you're taking the difference between two temperatures (and Celsius and Kelvin give the same value to each progressive unit of temperature, as opposed to Fahrenheit), the answer is still correct.

 

[WillJ]

It all looks right to me, except the units of temperature are in Kelvin, but since you're taking the difference between two temperatures (and Celsius and Kelvin give the same value to each progressive unit of temperature, as opposed to Fahrenheit), the answer is still correct.

Yep. Luckily our teacher generally isn't so tricky as to give us °F.

 

[Yom]

Yep. Luckily our teacher generally isn't so tricky as to give us °F.

When I first read that I thought you were being witty, using "°F" as "an F."

 

[Perfection]

EDIT: IIRC, Temperature measures the average kinetic energy of the molecules or atoms. Of course, temperature itself isn't given in joules or even a unit of energy.

That's not temperature, temperature is far more complex. In a gas this does closely approximate temperature but it is not universally true A good example is liquid water where a lot of the heat stored is in the form of electric potential energy . Water being a polar molecule has a + and - end. Often the positive end will line up with the negative end forming a hydrogen bond. When temperature increases the molecules move around more and the + and - ends are moved away, which requires a lot of energy.


Here's more on wikipedia for the curious to see what temperature is.
http://en.wikipedia.org/wiki/Temperature

 

[col]

Heat is energy that is transferred from a hot object to a colder one.

Internal Energy is the sum of all the kinetic and potential energies of a system.
Temperature is an index of the average internal energy per particle in a system.

 

[Mise]

I was always taught that wherever there was a T in an thermodynamics equation, stick a k in front of it (Boltzmann's constant) so that the equation makes sense. I don't think this is a thermo question, btw; judging by the units and the equation required, I'd call it a Chemistry question. You can have it back .

 

[Babbler]

I was always taught that wherever there was a T in an thermodynamics equation, stick a k in front of it (Boltzmann's constant) so that the equation makes sense. I don't think this is a thermo question, btw; judging by the units and the equation required, I'd call it a Chemistry question. You can have it back .

Yes it is; in fact, I remember doing problem just like this one in Chemistry 534 (high school).

 

[WillJ]

It's thermochemistry. Usually considered a branch of thermodynamics, I would think.

Heat is energy that is transferred from a hot object to a colder one.

That just begs the question of what "hot" and "colder" mean.

Internal Energy is the sum of all the kinetic and potential energies of a system.
Temperature is an index of the average internal energy per particle in a system.

Is it really that simple? I'd think, then, that degrees of temperature would correlate perfectly with joules-per-moles, and I don't think that's true. (Edit: Due mostly to specific heats, like Perf says in the post below.)

Perf's much more complicated link (which I'm too lazy to actually read) and explanation jive with me better.

I was always taught that wherever there was a T in an thermodynamics equation, stick a k in front of it (Boltzmann's constant) so that the equation makes sense.

I hope you were taught wrong.

 

[Perfection]

Temperature is an index of the average internal energy per particle in a system.

How can that be true if items have different specific heats? Isn't particle content roughly equivalent per mass when dealing with atomic matter?

 

[ainwood]

Because internal energy can be stored in different ways - for example hydrogen bonds which you referenced earlier can store more energy than van-der-waals bonds. Internal energy is the sum of the kinetic energy and the binding energy.

 

[Perfection]

Because internal energy can be stored in different ways - for example hydrogen bonds which you referenced earlier can store more energy than van-der-waals bonds. Internal energy is the sum of the kinetic energy and the binding energy.

Exactly my point! At zero degrees celcius a quanitity of liquid water and a hunk of ice of equal mass will have the same number of particles and the same temperature yet different internal energies.

 

[ainwood]

Hence why I said I thought it was a measure of average kinetic energy - two objects of different temperatures can transfer energy from one to another. The energy trnafser mechanism is via the atoms/molecules colliding with each other (or via radiation). The molecules hitting each other transfer energy based on the relative kinetic energy.

At any time, there are individual atoms with a wide-range of kinetic (and internal) energies. I guess the relation between average internal energy and temperature is that in the exaple you mentioned (liquid and solid water in equilibrium), the temperature of the mix can't go below zero or above zero until all the contents are in the same state.