Question

Two 84.5 g ice cubes are dropped into 30 g of water in a glass. If the water is initially at a temperature of 50 C and if the ice comes directly from the freezer at -300 C, what will be temperature of the drink when the ice and the water reach thermal equilibrium ? How much ice and how much water are present at thermal equilibrium ? Ignore the heat capacity of the glass and heat transferred to and from the environment.

Answer 1

final temperature will be 0 degree C

Total amount of ice will be

`m_(ice) = 182 g`

total amount of water

`m_(water) = 17 g`

Step-by-step explanation:

After thermal equilibrium is achieved we can say that

Heat given by water = heat absorbed by ice cubes

so we will have

Heat given by water to reach 0 degree C

`Q_1 = m_1s_1 \Delta T_1`

`Q_1 = 0.030(4186)(50 - 0)`

`Q_1 = 6279 J`

heat absorbed by ice cubes to reach 0 degree

`Q_2 = m_2 s_2 \Delta T_2`

`Q_2 = (0.169)(2100)(30)`

`Q_2 = 10647 J`

so we will have

`Q_2 > Q_1`

so here we can say that few amount of water will freeze here to balance the heat

`10647 - 6279 = mL`

`m = (10647 - 6279)/(335000)`

`m = 13 g`

so final temperature will be 0 degree C

Total amount of ice will be

`m_(ice) = 84.5 + 84.5 + 13`

`m_(ice) = 182 g`

total amount of water

`m_(water) = 30 - 13`

`m_(water) = 17 g`