Heat and Phase Change: Latent Heat?

Question

A thermos contains 145 cm3 of coffee at 85°C. To cool the coffee, you drop two 13 g ice cubes into the thermos. The ice cubes are initially at 0°C and melt completely. What is the final temperature of the coffee? Treat the coffee as if it were water. (See Table 12.2 and Table 12.3 for appropriate constants.)

http://kooch.gamedaemons.net/pictures/12-02tab.gif
http://kooch.gamedaemons.net/pictures/12-03tab.gif

Answer 1

Q = m c ΔT

Q = heat gained / lost (with no phase change)
m = mass
c = specific heat
ΔT = change in temperature, Tf - Ti where Tf = final temperature, Ti = initial temperature

Q = m L

Q = heat gained / lost during a phase change at constant temperature
m = mass
L = heat of fusion

We assume that the thermos creates a closed system, so the heat lost by the hot coffee = the heat gained by the ice.

( m_coffee ) ( c_coffee ) ( Tf - 85 ) = ( m_ice ) ( L_ice ) + ( m_ice ) ( c_water ) ( Tf - 0 )

Plug in the values and solve for the final temperature of the system, Tf.

Answer 2

Yes, in practice there will be some water which boils (900C is cherry red and a single 4 kg chunk of steel will boil a lot of water before it's surface cools down to 100C). In fact, if the answer is 195C, what is the boiling point of water??? If the first cut answer is greater than 100C, then you need to calculate what percentage of your water is boiled away (the only way to heat water above 100C is to pressurize it, with enough pressure, you can keep it liquid, but, even if it all turns to steam, it's temperature can not go about 100C unless it is under pressure). Since you can not heat steam to 195C without pressure and since the question does not say anything about pressure, you can assume that all this happens at STP or 1 atm of pressure. So, next calculation.... Taking 5 kg of water from 20C to 100C plus taking the latent heat of vaporization of 5 kg of water, how much heat is that? Compare this to the amount of heat lost by your piece of steel cooling from 900C to 100C. If the amount of heat consumed by the water (Cp + latent) is greater, then you know the equilibrium temperature will be less than 100C. If the amount of heat given off by the steel is greater, then you know the equilibrium temperature will be greater than 100C. Since the question asks the temperature of the steel-water mix and once the water boils away there is no more mix, it will be the temperature of the steel when the water is all turned to steam. hope this helps