Question

Brewed coffee is often too hot to drink right away. You can cool it with an ice cube, but this dilutes it. Or you can buy a device that will cool your coffee without dilution - a 240 aluminum cylinder that you take from your freezer and place in a mug of hot coffee.If the cylinder is cooled to -20 degreees celsius, a typical freezer temperature, and then dropped into a large cup of coffee (essentially water, with a mass of 500 ) at 85 degrees celsius, what is the final temperature of the coffee?

Answer 1

Answer:

75.2° C

Explanation:

Given:

mass of the coffee, M = 500

mass of the cup, m = 240

since the coffee is mostly water ,

specific heat of the coffee, C = 4.184 J/kg.°C

specific heat of the aluminium, C' = 0.902 J/kg.°C

The heat lost by the coffee will be transferred to the aluminium cup. The process of heat transfer will continue till the temperature of the coffee and the cup will be in equilibrium (or same)

i.e

Heat lost by the coffee = heat gained by the cup

or

MC(85 - T) = mC'(T - (-20))

where, T is the temperature at the equilibrium or the final temperature

on substituting the values, we get

500 × 4.184 × (85 - T) = 240 × 0.902 × (T - (-20))

or

T = 75.2° C

Hence, the final temperature of the coffee will be 75.2° C