Question

A piece of metal with a specific heat capacity of 0.460 J/gC at a temperature of 100.0C is dropped into an insulated container of water. The mass of water is 140.0 g and its temperature before adding the metal is 16.0C. The final temperature of the water is 17.6C. What is the mass of the metal?

Answer 1

The direction of the transfer of heat energy is dependent on the initial temperature of the metal and the water. Since the initial temperature of the metal is higher than the initial temperature of the metal, heat energy will be transferred from the metal to the water. Let’s use the following equation to determine the amount of heat energy that is transferred.

Q = mass * specific heat * ∆ T

For the iron, ∆ T = 100 – 17.6 = 82.4˚

For the water, ∆ T = 17.6 – 16 = 1.6˚

For the iron, Q = m * 0.460 * 82.4 = m * 37.904

For the water, Q = 140 * 4.186 * 1.6 = 937.664 J

m * 37.904 = 937.664

m = 937.664 ÷ 37.904

The mass of the metal is approximately 24.7 grams.

Answer 2

the mass of the metal is

Mm=24,7378 grams

Step-by-step explanation

the explanation can be found in the attached picture.

The mass of the metal was calculated under the assumption that

- the heat capacity of the water and the metal do not change with temperature

- the metal does not react with the water