Consider melting of a one-dimensional slab of ice due to a temperature of 10 C imposed on one end of the ice. Assuming standard properties

Consider melting of a one-dimensional slab of ice due to a temperature of 10 ºC imposed on one end of the ice. Assuming standard properties of water, please (a)
calculate and plot the location of the melting front as a function of time, up to 1 minute.

a.determine the length of ice melted in 1 minute. 

b. determine how much does the imposed temperature need to be increased by in order to double the amount of ice melted in 1 minute. Is this more than or less than (or equal to) double the present value of 10 ºC for the imposed temperature? Why?
 For the same problem as above, a scientist claims to have an additive that can increase the heat capacity of water without affecting any other properties. Will doing so increase the rate of melting of ice? To evaluate this, please plot the length of ice melted in one minute as a function of heat capacity, between values of 4184 J/kgK and 8000 J/kgK