A waiter pours V_0 = 500 ml of hot coffee (mostly water, at T_H = 95degree C whi

Question

A waiter pours V_0 = 500 ml of hot coffee (mostly water, at T_H = 95degree C which could cause severe scalding) filling a ceramic mug (at room temperature-please estimate T_R for this problem). The mass of the mug is equal to half the mass of the coffee it holds. (a) What is the final temperature T_M of this cup of coffee? (b) Do you think it would still be too hold to drink, or is it cool enough to drink? (c) Now, add a 50 g chunk of ice (M_Ice) to the cup. After it has melted, what is the final temperature T_C of the coffee? (Note: the coffee now has a volume V_F = 550 ml, and don't forget to include the influence of the mass of the mug.) Do you think it's too hot to drink, too cool, or about right?

Explanation / Answer

Vo = 500 ml

mass of coffee , m0 = 500 ml * 1 gm/ml = 500 gm

mass of mug , m = 500 * 0.5 = 250 gm

specific heat of coffee , So = 4.186 J/(gm.degree C)

specific heat of mug , Sm = 0.61 J/(gm.degree C)

Th = 95 degree C

TR = 25 degree C

let the final temperature is Tf

heat lost by coffee = heat gain by cup

4.186 * 500 *( 95 - Tf) = 0.61 * 250 * (Tf - 25)

solving for Tf

Tf = 90.25 degree C

the final temperature of the coffee will be 90.25 degree C

part b)It is very hot to drink.

part c) let the final temperature is Tf

heat gain by ice = heat lost by coffee + heat lost by mug

334 * 50+ 4.186 * 50 * Tf = 500 * 4.186 *( 90.25 - Tf) + 250 * 0.61 * (90.25 - Tf)

solving for Tf

Tf = 75.7 degree C

the final temperature will be 75.7 degree C

d) this is about right temperature to drink coffee.

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