You take a 50 g glass coffee mug from the dishwasher followingthe dry cycle. You

Question

You take a 50 g glass coffee mug from the dishwasher followingthe dry cycle. You use a dishcloth because the temperature ofthe mug is 90 C. You fill the mug with 250 g of cold waterfrom the refrigerator. The temperature of the water is 5C. Assume no heat is lost to either the air, the kitchencounter, or to your hand. What will be the final temperature if thecup, and of the water in it? [Specific heats: glass,837 J/(kg)(C); water, 4186 J/(kg)(C) ]

Explanation / Answer

Since all the heat is consumed in changing the temperature of thewater and glass, you can do an energy balance among the two: Energy change in glass = -(energy change in water) mg*cg*(Tg2-Tg1) = -mw*cw*(Tw2-Tw1) , where g refers to glass, w refers to water, and c's are the respectivespecific heats, and T's are the before and after temperaturesrespectively. Since everything is at the same temperature in the end, Tg2 = Tw2and you have: mg*cg*(Tw2-Tg1) = -mw*cw*(Tw2-Tw1) You should now be able to solve for Tw2: => mg*cg*Tw2 - mg*cg*Tg1 = mw*cw*Tw1 - mw*cw*Tw2 => mg*cg*Tw2+mw*cw*Tw2 = mw*cw*Tw1 + mg*cg*Tg1 => Tw2 = (mw*cw*Tw1 + mg*cg*Tg1)/(mg*cg+mw*cw) = [(0.250kg)*(4186J/kg-C)*(5C) +(0.050kg)*(837J/kg-C)*(90C)]/[(0.050kg)*…(0.250kg)*(4186J/kg-C)] = 8.27C good luck, sammy

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