Consider the following specific heats of metals. Metal Specific Heat Aluminum 0.897 J/(g°C) Magnesium 1.02 J/(g°C) Lithium 3.58 J/(g°C) Silver 0.237 J/(g°C) Gold 0.129 J/(g°C) If the same amount of heat is added to 25.0 g of each of the metals, which are all at the same initial temperature, which metal will have the lowest temperature?

Lithium

Explanation:

The specific geat capacity of a substance is the energy required to raise 1 unit of that substance by one degree.

Heat energy (Q) = mc∇t

Q = heat energy

M = mass of the substance

c = specific heat capacity

∇t = change in temperature of the substance

Generally, increase in the specific heat capacity will lead to a lower final temperature likewise decrease in the specific heat capacity will lead to increase the final temperature of the substance.

From the data above, we can take just two specific heat capacity and test this theory.

Assuming we have a

Mass = 25g

Heat energy applied (Q) = 1 J

Initial temperature (T1) = 10°C

Final temperature (T2) = ?

Q = mc∇t

Q = mc (T2 - T1)

For Lithium, specific heat capacity = 3.58J/g°C

1 = 25 × 3.58 (T2 - 10)

Solve for T2

1 = 89.5 (T2 - 10)

1 = 89.5T2 - 895

89.5T2 = 896

T2 = 896 / 89.5

T2 = 10.011°C

For Magnesium (Mg) specific heat capacity = 1.02J/g°C

Q = mc∇t

1 = 25 × 1.02 × (T2 - 10)

1 = 25.5 (T2 - 10)

1 = 25.5T2 - 255

Solve for T2

25.5T2 = 256

T2 = 10.039°C

Notice the trend that decrease in the specific heat capacity leads to increase in the final temperature.

Try and continue for the elements and see how it works.

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