We drop a cube of ice into a glass of water. The mass of the cube of ice is 33.1 g and its initial temperature is - 10.2∘C. The mass of the water is 251 g and its initial temperature is 19.7∘C. What is the final temperature of the water after all of the ice has melted?

Answer: The final temperature (T) will be;

16.23°c

Explanation: To find the final temperature of any mixture of substance with an initial temperature use the formula;

M1c (T-T1) + M2c (T-T2) = 0

c is the specific heat capacity of the two different substance, but because ice and water are the same, we assume c to be 1

T = final temperature of the mixture

T1 = initial temperature of the ice = - 10.2°c

T2 = initial temperature of the water = 19.7°c

M1 = mass of ice = 33.1g

M2 = mass of water = 251g

Using the formula above

33.1 (T - (-10.2)) + 251 (T-19.7) = 0

Solving out the bracket

33.1T + 337.62 + 251T - 4944.7 = 0

Collecting like terms to both side of the equation and solving

33.1T + 251T = 4944.7 - 33.62

284.1T = 4607.08

T = 4607.08:284.1 = 16.23°c