How Do You Calculate Thermal Equilibrium and Ice Formation Times?

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SUMMARY

This discussion focuses on calculating thermal equilibrium and ice formation times using principles of heat transfer and the Ideal Gas Law. A copper slug heated to 3120°C is analyzed for its final temperature when placed in water at 12°C, considering the heat capacities of the materials involved. Additionally, the discussion covers the calculation of ice formation from water at 6°C using radiation principles, and the Ideal Gas Law is applied to determine the final pressure of oxygen gas in a cylinder after changes in temperature and volume. Key formulas and concepts are emphasized for accurate calculations.

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  • Understanding of heat transfer principles
  • Knowledge of black body radiation and emissivity
  • Familiarity with the Ideal Gas Law (PV=nRT)
  • Basic thermodynamics concepts
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  • Study heat transfer calculations involving specific heat capacities
  • Learn about black body radiation and its applications in thermodynamics
  • Review the Ideal Gas Law and its derivations for pressure, volume, and temperature changes
  • Explore practical examples of thermal equilibrium in various materials
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Students and professionals in physics, engineering, and environmental science who are involved in thermal analysis, heat transfer calculations, and gas behavior under varying conditions.

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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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