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>

 

[rwisz]

Hi Peter,

First of all, great job trying to solve this problem using the principles of thermal physics! Your approach is generally correct, but there are a few things that could have led to the incorrect answer.

Firstly, in your initial equation, you have Q/600 on one side and the mass change and latent heat of vaporization on the other side. However, Q/600 represents the rate of heat transfer, not the total amount of heat transferred. So, instead of dividing the mass change by 600, you should divide by the time (600 seconds) to get the rate of change in mass. This will give you the correct equation:

Q/600 = (0.0463/600) x 1.99 x 10^5

Another potential issue is the units. In thermal physics, it is important to use consistent units throughout the problem. In this case, you should convert the mass change from grams to kilograms, so you would have 0.0463 kg instead of 46.3 g. This will give you the correct units for the final answer, which should be in watts (J/s).

Lastly, it is important to pay attention to the units of the final answer. In this case, you are trying to find the rate at which the surroundings are heating the beaker, which would be in watts. However, your final answer is currently in joules per second (J/s). To convert to watts, you need to divide your current answer by 600, since 600 seconds is the time interval you are considering. This will give you the final answer in watts.

I hope this helps clarify any confusion you had. Keep up the good work in your studies of thermal physics!

Best,