How Do You Calculate Thermal Equilibrium and Ice Formation Times?

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The discussion revolves around calculating thermal equilibrium and ice formation times, focusing on three distinct problems. The first problem involves a copper slug heated to 3120C being dropped into water, prompting questions about the final equilibrium temperature. The second scenario discusses freezing water using radiation on a cold night, with participants expressing confusion about the starting point for calculations. The third problem applies the ideal gas law to determine the final pressure of oxygen in a cylinder after changes in temperature and volume. Participants suggest reviewing heat transfer and black body radiation concepts to aid in solving the first two problems.
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1. Heat Transfer
A copper slug whose mass mc is 75g is heated in a laboratory oven to a temperature T of 3120C. The slug is then dropped into a glass beaker containing a mass mw =220g of water. The heat capacity Cb of the beaker is 45 cal/K. The initial temperature Ti of the water and the beaker is 120C. What is the final temperature Tf of the slug, the beaker, and the water when thermal equilibrium is reached?

Would this look about right?
mc(water)+mc(copper calorimeter) +mc (beaker) = 0.

2. How to Make Ice Without a Refrigerator
On a clear moonless night, the sky acts like a blackbody radiator at a temperature Ts=
-230 C. You thermally insulate a container from the ground (by placing a poorly conducting layer of straw beneath it). Then you pour water into the container, forming a thin, uniform layer with mass m=4.5 g, with surface area A = 9.0 cm2 and depth= 5.0 mm. The emissivity is .9, and initial temperature 6.00C. Find the time required for the water to freeze via radiation.

On this one I am super lost, no idea from where to start.

3. The Ideal Gas Law
A cylinder contains 12 L of oxygen at 200C and 15 atm. The temperature is raised to 350C, and the volume is reduced to 8.5 L. What is the final pressure of the gas in atmospheres?

Same as the other one, if you guys/gals can point me to the right direction formula wise that would be great.
 
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I didn't have time to read 1 and 2 but for 3 you should be able to use

intial PV/T = final PV/T
 
Hermite said:
I didn't have time to read 1 and 2 but for 3 you should be able to use
intial PV/T = final PV/T
Does this look about right?
P(12)/200=P(8.5)/350
 
Goalcard said:
Does this look about right?
P(12)/200=P(8.5)/350

yes no maybe so? :biggrin:
 
you're on the right track.. How about including your initial pressure P_i and solving for final pressure P_f
 
Ouabache said:
you're on the right track.. How about including your initial pressure P_i and solving for final pressure P_f
final pressure would be 37.059?
 
Goalcard said:
final pressure would be 37.059?
Yeah? any tips on the first two?
 
Goalcard said:
Yeah? any tips on the first two?
Maybe throw me a formula, that would help me a lot, it's due tomorrow(Wednesday)
 
Goalcard said:
final pressure would be 37.059?
Looks good to me..

On the first two, if I were assigned these questions, instead of guessing which formula to use, I would review material on heat transfer and black body radiation. Here is a starting point ref
 
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