Why Did My Calculation of the Heat Transfer Rate in Thermal Physics Go Wrong?

[Peter G.]

Hi

The mass of liquid nitrogen in an open beaker is found to have decreased by 46.3 g in 10 minutes. If the S.L.H of vaporization of nitrogen at is boiling point is 1.99 x 10⁵ J/Kg, at what rate were the surroundings heating the beaker?

This is what I did:

Q / 600 = 0.0463 / 600 x 1.99 x 10⁵

I then got: Q / 600 = 15.35616667

But I got the answer wrong because I passed the 600 to the other side multiplying.

I am confused as to why I can't do so...

My best thought so far is that at the beginning I should do:

P = 0.0463 / 600 x 1.99 x 10⁵

But can anyone explain why?

Thanks,
Peter G.

 

[gneill]

Why would you "pass the 600 to the other side multiplying"?

Q/600 is presumably meant to reflect the total heat Q divided by the time in seconds, which would give you the rate that heat is absorbed. You've shown the 600 on the right hand side of your expression:

Q / 600 = 0.0463 / 600 x 1.99 x 10⁵

That right hand side *is* the calculation for the rate, P = Q/600s.

 

[Peter G.]

Oh, ok, I get it, but the 600 dividing by the mass is correct, right?

And if you could help me with one other thing...

How do I derive the equation PV = nRT?

Well, to be more specific, how do we get PV / T combining all the laws: (Boyle's, Gas...)

Thanks

 

[gneill]

Oh, ok, I get it, but the 600 dividing by the mass is correct, right?

One way to verify that you're formula is correct is to keep the units with the values and make sure that the units work out as expected.

You know that you're looking for the rate of heating. Heat is specified in Joules, time is in seconds, so the rate is Joules per second (which are the units for Power, and J/s = Watts).

You first calculated the heat (Joules) by multiplying the mass (kg) by the heat of vaporization (Joules/kg). Then you divided by the time (seconds), yielding

kg x J/kg /s = J/s = W

So the units work out as expected and you can have confidence in your calculation.

And if you could help me with one other thing...

How do I derive the equation PV = nRT?

Well, to be more specific, how do we get PV / T combining all the laws: (Boyle's, Gas...)

Thanks

Take a look at the Wikipedia article for the combined gas law and the one for the ideal gas law.

<http://en.wikipedia.org/wiki/Combined_gas_law>
<http://en.wikipedia.org/wiki/Ideal_gas_law>