Question

Between periods of a hockey game, an ice resurfacing machine spreads 300.0L of hot water (40*C) across a frozen ice skating rink. How much heat does the water lose as it cools to freezing point, freezes, and drops further to -10*C?

Use the density of water at 40*C (.992g/ml) to more accurately determine the number of grams.

Answer 1

Given: Volume of water = 300.0 L = 3.0 * 10 ⁵ mL

Initial temperature of water = 40 deg C

Final temperature of water = - 10 deg C

Density = 0.992 g / mL

Solution

We use calorimetric formula to calculate heat given by the water when it cools

q = m * C * Delta T

and q = m * Delta Hfus

Here Delta Hfus = heat of fusion of ice

Specific heat of water = 4.184 J / g deg C

Specific heat of ice = 2.03 J / g deg C

Lets calculate mass of water

We know,

Density = mass/ volume

Mass = density* volume

= 0.992 g/mL * 3.0 * 10⁵ mL

= 2.98 * 10⁵ g

Here are three transition

1. q1( From 40 deg C to 0 deg C )

= m * C_water * Delta T

1. q2 (From 0 deg C to 0 deg C) = Delta Hfus * mass of ice
2. q3 (From 0 deg C to -10 deg C ) = m_ice * C_ice * delta T

q = q1 + q2 +q3

= (2 .98 * 10⁵ g * 4.184 J / g deg C * ( 0