Question

As a hobby, Prof. Andrew brews his own beer. This involves preparing the proper media (wort, a mixture of water and malt sugars, which has a specific heat of 3822 J/kg K) in which yeast can thrive. Key in this process is killing off wild bacteria as much as possible in the media, so that the yeast that is added performs the majority of the fermentation. Boiling the wort for an extended period of time (usually at least 30 minutes) is sufficient to limit these bacteria. This results in a mass of 9 kg of concentrated wort at approximately 99 degrees Celsius. This temperature would easily also kill the yeast that makes beer possible. The yeast can only be added when the liquid is a maximum of 20 degrees Celsius (and at lowest 3 degrees Celsius). If Prof. Askew deploys a heat exchanger which quickly removes 2.5 x 10^6 J of heat in around five minutes, then is it safe to pitch the wort? What if he adds the liquid to an additional 11.4 kg of water at 10 degrees Celsius, is it safe?

I need a conceptual answer to this, thanks for the help!

Answer 1

given

a specific heat of 3822 J / kg K = C

Boiling the wort for an extended period of time (usually at least 30 minutes)

9 kg of concentrated wort at approximately 99 degrees Celsius

the liquid is a maximum of 20 degrees

Celsiusat lowest 3 degrees Celsius 2.5 X 10⁶ J of heat in around five minutes

an additional 11.4 kg of water at 10 degrees Celsius

the heat lost in cooling is = m C dT

= 9 X 3822 X ( 99 - 20 )

= 2717442 J

removing 2.5 X 10⁶ J of heat in around five minutes is insufficient as a heat remove is

required to bring solution to 20^oC

and heat gained by water is = m C dT

= 11.4 X 4184 X 10

= 476976 J

so it is separately not sifficient to bring the mixure back to the 20^oC

so as a whole the addition heat is sufficient to bring back the solution below 20^oC