B$1.$ Let$$s obtain the equation for the final temperature of the water$/$block system. The first law of

thermodynamics states that the flow of heat is just the transfer of internal energy. If we assume

that the water block system is isolated, what relationship between Qwater and Qblock?

B$2.$ Rewrite this equation in terms of the heat capacities and initial temperatures of water and the

block, and the final temperature. Solve for the final temperature. Does your answer make sense

when compared with A$3?$

B$3.$ What if the block started at a higher temperature than the water, and the water was just

below boiling temperature. What would be the analogue of the equation you wrote in the first

step of B$2?$ You may assume that there is so much water there is no concern that all of it will

boil off.

C$.$ Predict the temperature

C$1.$ You$$ve been given a $($cylindrical$)$ metal mass with some unknown heat capacity. You have

liquid nitrogen available to you to cool the cylinder, and a beaker to fill with some amount $($your

choice$)$ of water. Your goal is to predict the final temperature of the water, after the nitrogen$-$

cooled cube is added to it$.$ You are given that:

The latent heat of vaporization of nitrogen is $47\mathrm{.}8$ kcal$/$kg$=199995\mathrm{.}2$ J$/$kg

The density of liquid nitrogen is $808\mathrm{.}4$ kg$/$m$3$

C$2.$ Before you put the cylinder in liquid nitrogen, make sure you have a string tied around

notch in the center of the cylinder, or some other way of getting the cylinder out of the nitrogen

after you put it in$.$

C$3.$ Call your TA over when you obtain an experimental value for the final temperature, so that

your TA can see that your measurement is correct. Then compute your percent error