Question

To make ice water, I mix 200 g of water at 25.0 degrees celcius with 100 g of ice cubes at -15.0 degrees celcius. Water density is 1.00 g/cm^3, and the container perfectly insulates the system from the enviroment. Thermal equilibrium is eventually reached. Assume that all the ice must reach 0 degress celcius before any ice begins to melt. (a) determine (i) if any unmelted ice remains, and if so, the mass of the remaining unmeltd ice, and (ii) the final temperature of the mixture.

Answer 1

Mass of water = M_water= 200g

Mass of Ice cubes= M_ice = 100g

Temp of water = 25degree cel

Temp of ice = -15 deg cel

Density of water = 1.00g/cm^3

When two or more objects at different temperaturesare brought together in an isolated environment, they eventually reach the same temperature by the process of heat exchange. That is the warmer materials transfer heat to colder materials until their temperatures are the same.

According to the law of conservation of energy ,

Heat gained by ice = Heat lost by water

M_ice L_f + SM_ice (T_final - 0degree C) = SM_water (T _initial - T_final )

S =1 is specific heat and L_f is latent heat of fusion = 79.7 cal/gm

(a) The mass of ice remained will be 49.8 grams.

(b)The final temperature of the mixture will be 0 degree cent.