# Is the metal in the following situation most likely Iron, Aluminum, or Silver?A 5.0 g sample of a metal is heated to 80.0oC and placed in a 100. g sample of water. The water temp rises from 20.0oC...

Is the metal in the following situation most likely Iron, Aluminum, or Silver?

A 5.0 g sample of a metal is heated to 80.0^{o}C and placed in a 100. g sample of water. The water temp rises from 20.0^{o}C to 20.6^{o}C

Please show work and explain how to do it

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### 1 Answer

The amount of heat in a given object can be found by using the formula Q = m * Cp * delta T where

Q = heat in Joules

m = mass in grams or kilograms

Cp = specific heat of the substance

delta T = change in temperature

When a heated object is put into water, the final temperature is the same for the object and the water. The heated object cools and transfers its heat energy to the water, raising the temperature of the water.

Therefore:

Q (object) = Q (water)

and

m (object) * Cp (object) * delta T (0bject) = m (water) * Cp(water) * delta T (water)

Substitute in your values and you get

5 * Cp (object) * (80 - 20.6) = 100 * 1 * (20.6 - 20)

Solve for Cp

Cp = 60/297 = 0.202cal/g *degree C

If you consult a table of specific heats you will find:

Aluminum = .22

Silver = 0.06

Iron = 0.11

Your answer is closest to aluminum