2 replies to this topic

[processengineerx]

Below are the two questions related to heat transfer dynamics, which may interest process engineers,

1) How much time would be required for an ice cube (8 cm3) to completely disappear when dropped in 1000 cm3 water at 25 C & 1 atm? What would be the final temperature of water?
2) How much time would be required for the temperature of mixture to get stablized, when 0.5 M. Tons of water at 50 C are mixed in 1.0 M. Tons of water at 25 C?

I hope that every process engineer would enjoy recalling the old days while solving the questions.

[alcir grohmann]

It's interesting !! Well...about final temperature, an energy balance shall solve the problems. The real problem is the time !! I believe that to calculate the time you should have some other informations (degree of agitation, etc). It's not so easy...

Regards

Alcir Grohmann

[mansari]

Interesting. The second part of the first question is straight forwars. Calculation of final temperature. It is 8 cc of ice which means 7.4 g at a density of 0.92 g/cc. Heat of fusion of ice is 334 kJ/kg or 80 kCal/kg. Therefore total heat transferrable to water is 0.6 kCal. Water has a mass of 1 kg. Assuming a system where no heat flows out, temperature drop in water would be 0.6 C and final temperature would be 24.4C

 

However the first part is tricky. In order to calculate heat rate, you need to apply Fourier's equation dQ/dt = kA/dT/dx where k is the thermal conductivity,  A is the area of contact. In this case, area of contact is deminishing as ice is melting. Therefore rate of heat transfer keeps changing with time.

 

I would appreciate if the originator share the anwers alongwith the calculations for the knowledge of the members