Calculating Heat Transfer in Mercury and Water: Homework Problem and Solution

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SUMMARY

The discussion focuses on calculating heat transfer in a scenario involving mercury and liquid nitrogen. Susan has 3.50 cubic centimeters of mercury, and the calculations involve determining the heat energy required to vaporize mercury at 500°C, which was found to be 45137.6 J. Additionally, the discussion addresses the mass of liquid nitrogen boiled away when cooling mercury to -196°C, emphasizing the need for the heat of vaporization of nitrogen and the heat of fusion of mercury for accurate calculations.

PREREQUISITES
  • Understanding of specific heat capacities, specifically for solid, liquid, and gaseous mercury.
  • Knowledge of the heat of vaporization and heat of fusion concepts.
  • Familiarity with the formula (delta)Q=mc(delta)T for heat transfer calculations.
  • Basic principles of thermodynamics related to phase changes.
NEXT STEPS
  • Research the heat of vaporization of nitrogen for accurate calculations.
  • Learn about the heat of fusion for mercury to understand phase changes.
  • Explore advanced thermodynamic equations for multi-phase heat transfer problems.
  • Investigate real-world applications of heat transfer calculations in engineering contexts.
USEFUL FOR

Students in physics or engineering courses, educators teaching thermodynamics, and professionals involved in heat transfer calculations or material science.

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Homework Statement


One day Susan collected the mercury from the thermometers around her house and found she had 3.50 cubic centimeters of mercury (density= 13.6 g/cm^3) at room temperature of 28C. She places the mercury in a small bag and drops it into liquid nitrogen (-196C).a. Calculate how much heat energy would be required to change this frozen block of mercury into vaporized mercury at 500C. The specific heat of solid mercury is 134, the specific heat of liquid mercury is 139, and the specific heat of gaseous mercury is 104.

b. What mass of liquid nitrogen was boiled away when she lowered the mercury's temperature to -196C?

Homework Equations


(delta)Q=mc(delta)T

The Attempt at a Solution



I did part a. I got as an answer 45137.6J of energy. However, I'm not quite sure how to set up part b. What equation should I use?EDIT: this seems to be related to the next question:

A construction worker on a rooftop 20m high drops a hot .150kg iron rivet at 500C into a bucket containing 6kg of water at 20C. Assuming no heat is lost to the surroundings or the bucket, and that no water splashes out, what is the final temperature of the rivet and the water?

I'm just not really sure which equation to use...
 
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You will need to know the amount of heat needed to change a kg of liquid nitrogen into nitrogen vapour. This would be called the "heat of vaporization" of nitrogen and should be available in Wikipedia.

In the first part, you would also need the heat of vaporization of mercury. And the heat needed to liquefy solid mercury (heat of fusion).
 

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