Question

(a) You took two 49-gram ice cubes from your -14C kitchen freezer and placed them in 201 g of water in a thermally insulated container. If the water is initially at 24C, what is the final temperature at thermal equilibrium? (b) What is the final temperature if only one ice cube is used? Hint: Watch out for the different possibilities!

Answer 1

a)specific heat capacity of water = 4.2

specific heat capacity of ice = 2.03

energy required to bring the water to 0C = 4.2*201*24

=20260.8 J

energy reqired to bring ice to 0C = 2.03*2*14*49

=2785.16 J

energy required for both the cubes to melt = 334*2*49

=32732

now since 32732+2785.16 > 20260.8

hence the amount of energy required for the ice cubes to melt is greater than that required for the water to come to 0C.

hence the final temperature is 0C.

if there is only one ice cube,

enthalpy of fusion = 16366

enthalpy of reaching to 0C from -14C = 1392.58 J

so total energy required for the ice to melt = 16366 + 1392.58

=17758.6 J

so let the final temperature be T. so ,

conserving energy,

energy lost=energy gained

or 4.2*201*(24-T) = 17758.6 + 4.2*49*(T-0)

or T=2.38 C