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 200 aluminum cylinder that you take from your freezer and place in a mug of hot coffee.

q)If the cylinder is cooled to -20C, a typical freezer temperature, and then dropped into a large cup of coffee (essentially water, with a mass of 500g ) at 85C, what is the final temperature of the coffee?answer in 2 sig figs and answer in Celsius.

Answer 1

`T_f=57.21\ ^(\circ)C`

Step-by-step explanation:

Given:

• mass of aluminium,
  `m_a=0.2\ kg`

• initial temperature of the aluminium cylinder,
  `T_(ia)=-20\ ^(\circ)C`

• mass of coffee,
  `m_c=0.5\ kg`

• initial temperature of coffee,
  `T_(ic)=85\ ^(\circ)C`

• specific heat of coffee (assuming water),
  `c_w=1000\ J.kg^(-1).^(\circ)C^(-1)`

• specific heat of aluminium,
  `c_a=900\ J.kg^(-1).^(\circ)C^(-1)`

When the coffee and the aluminium cylinder come in contact then heat released by the coffee is equal to the heat gained by the aluminium.

Mathematically:

`Q_c=Q_a`

`m_c.c_w. (T_(ic)-T_f)=m_a.c_a.(T_f-T_(ia))`

`0.5* 1000* (85-T_f)=0.2* 900* (T_f-(-20))`

`42500-500* T_f=180* T_f+3600`

`T_f=57.21\ ^(\circ)C` is the final temperature of agreement.