Use the specific heat capacity that you calculated for granite to determine how many grams of granite at the initial temperature of 80 °C must mix with 3,000 g of water at the initial temperature of 20 °C to result in a final system temperature of 20.45 °X. (Hunt: Start by calculating how much heat energy is needed to change the water’s temperature by 0.45 °C). Show your work. Use the Gizmo to check your answer.

Explanation:

specific heat of granite s = .79 J / g / k

let the mass of granite = m

heat lost by granite = heat gained by water

heat lost = mass x specific heat x drop in temperature

= m x .79 x (80 - 20.45)

heat gained by water

= 3000 x 4.186 x (20.45- 20)

heat lost by granite = heat gained by water

m x .79 x 59.55  =  3000 x 4.186 x .45

m = 120.12 g .

The mass of granite is approximately equal to 120 g.

The specific heat capacity refers to the amount of energy required or needed to raise the temperature of 1 gram of a material or substance by 1° C.

Let assume that:

The heat energy gained by water can be calculated using the formula:

Q = mcΔT

where;

m = mass = 1000 g

c = specific heat = 4.183 J/g° C

ΔT = change in temperature

Q = 1000 g × 4.183 J/g° C × (2.93 - 0)° C

Q =  1000 g × 4.183 J/g° C × (2.93) ° C

Q = 12256.19 J

Q = 12.256 kJ

The next step is to determine the specific heat of granite.

Since;

The heat gained by water = Heat lost by granite.

The heat lost by granite = 12.256 kJ

Using the relation;

Q = mcΔT

Making (c) the subject of the formula:

The specific heat of granite = 0.795 J/g° C

Recall from the given parameters;

∴

Again, heat gained by water = heat lost by granite

To determine the mass of granite, make the subject of the formula;

i.e.

Therefore, we can conclude that the mass of granite is approximately equal to 120 g.

Learn more about specific heat capacity here:

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