A copper bowl of mass m1 contains a mass m2 of water, both at temperature T (whi

Question

A copper bowl of mass m1 contains a mass m2 of water, both at temperature T (which is below the boiling point of water). A very hot copper cylinder with mass m3 is dropped into the water, causing the water to boil, with a mass m4 being converted to steam. The final temperature of the system is 100°C. Neglect energy transfers with the environment. (Use any variable or symbol stated above along with the following as necessary: cw for the specific heat of water, cc for the specific heat of copper, and Lv for the latent heat of vaporization of water. Note that the c, w, and v are lowercase. Assume the masses are measured in grams, temperatures in °C, specific heats in cal/g · °C, and the heat of vaporization of water in cal/g.) (a) How much energy is transferred to the water as heat? Qwater = c (b) How much to the bowl? Qbowl = c (c) What is the original temperature of the cylinder? Ti = c

Explanation / Answer

(a) Heat transferred to water, Qwater = m2*cw*(100-T) + m4*Lv cal

(b) Heat transferred to the bowl, Qbowl = m1*cc*(100-T) cal

(c) Heat lost by cylinder = heat gained by bowl + heat gained by water

m3*cc*(Ti-100) = m2*cw*(100-T) + m4*Lv + m1*cc*(100-T)

Ti = 100 + (m2*cw*(100-T) + m4*Lv + m1*cc*(100-T))/m3*cc

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