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

[Nimbalo]

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...

 

[Delphi51]

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).

 

[nlightner]

For part b, you can use the equation Q=mc(delta)T, where Q is the heat energy required to change the temperature of the liquid nitrogen, m is the mass of the liquid nitrogen, c is the specific heat of liquid nitrogen, and (delta)T is the change in temperature. You can set up this equation for the change in temperature from -196C to the boiling point of liquid nitrogen, which is -196C. Then, you can solve for the mass of liquid nitrogen that was boiled away.

For the construction worker problem, you can use the same equation, Q=mc(delta)T, for both the iron rivet and the water. Set up two separate equations, one for the iron rivet and one for the water, and then solve for the final temperature using the equation Q = Q. Since the final temperatures of both objects will be the same, you can set up the equations as Q1 = Q2 and solve for the final temperature.