Question

An open container holds ice of mass 0.575kg at a temperature of -12.2?C . The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 780J/minute . Part A How much time tmelts passes before the ice starts to melt? Part B. From the time when the heating begins, how much time does it take before the temperature begins to rise above 0 Degrees Celsius

Answer 1

Given that,

Mass of ice to be melted = m = 0.575 kg

Intial temp of ice = Ti = -12.2 deg C, then T = ( 0 - (-12.2) = 12.2 deg C

Heat supplied = Q(s) = 780 J/min

We know that, specific heat of ice = Cp = 2100 J / kg K and Heat of fusion is = 334 x 10³ K /kg

For the ice to start melting the temperature should be 0 deg C.

Lets assume that the amount of heat required to change the temp from -12.2 deg to 0 deg cent be Q1. And Q2 be the amount of heat required to melt the ice.

We know that Q1 will be ;

Q1 = m Cp T = 0.575kg x 2100 J/kg-K x (12.2)

Q1 = 14731.5 Joules

Q2 will be given by:

Q2 = m Hf = 0.575 x 334 x 10³ J/kg = 192050 Joules

Part (A) So time passes/ required before ice starts to melt = Q1 / Rate of heat supplied

t_melts = 14731.5 Joules / 780 J /min = 18.88 min = 19 min

Hence tmelts = 19 minutes.

Part (B)

total heat required to be transmitted to ice for raising temp. from -12.2 deg C to 0 deg celsius so that melting of ice can take place will be:

Q(total) = Q1 +Q2 = 14731.5 + 192050 Joules =206781.5 Joules

So time it take before the temperature begins to rise above 0 Degrees Celsius = Q(total) / Rate of heat supplied = 206781.5 J/ 780 J min =265 minutes

Hence t = 265 minutes.