There is a keg of beer that has a diameter of 0.2 meters and a height of 0.6 meters. The keg has an initial temperature of 20 degrees Celsius and needs to be cooled to a temperature of 5 degrees Celsius. There are two options to cool the keg. The first option is to put the keg in a freezer that is at a temperature of -20 degrees Celsius with a convective coefficient of h = 200 W/(m^2 *K). The second option is to place the keg in an ice bath that is at zero degrees Celsius with a convective coefficient of h = 200 W/(m^2 *K). Which of the options will be faster and by how much time?

Assumptions:

• there is no heat transfer from the top or bottom of the keg (radial direction cooling)
• Beer is composed mostly of water
• Neglect the keg in the calculations since it has a high thermal conductivity