If heat is being added at a constant rate to a sample of ice (i.e., solid water)

Question

If heat is being added at a constant rate to a sample of ice (i.e., solid water), initially at -10°C, which graph best represents the plot of sample temperature vs. time over a two-minute period? You should further assume that it takes 10 seconds for the sample to reach 0°C from start.

You may find the following data helpful when deciding which graph is correct:

Specific heats for water: cliquid = 1.0 cal/g °C and cice = csteam = 0.5 cal/g °C
Latent heats for water: heat of fusion Lf = 80 cal/g and heat of vaporization Lv = 540 cal/g

1) If heat is being added to the sample at a constant rate of 90 cal/s, what is the mass of the sample? (2 points) Show your work (3 points)


Also... what would the graph (temp vs time) look like?


Please show work clearly... really having trouble with this stuff

Explanation / Answer

rate of Q = 90 cal/s

it is completed in 10 sec, so Q = 90*10 = 900cal

Q = msT + mL

m = Q/[sT + L]

here initial temp = -10C and final temp is 0C

s = 0.5 and L = 80

= 900/[0.5*10 + 80]

= 900/85

= 10.59 g

so mass of ice is 10.59 grams

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