A sample of unknown metal has a mass of 36.7 g. This metal was placed in boiling water at 96.0oC until the metal had reached the temperature of the water. The metal was then placed in a foam cup with 50.0 g of water in it at 20.0oC. The cup absorbs 42.0 J/oC, and the temperature of the water went up to 24.0oC. What is the specific heat of the metal?

heat lost be warm metal + heat gained by water + heat gained by foam cup = 0

[mass warm metal x specific heat metal x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] + [Ccup x (Tfinal-Tinitial)]
Substitute and solve for specific heat metal.
Post your work if you get stuck.

To find the specific heat of the metal, we can use the formula:

q = m × c × ΔT

Where:
q is the heat absorbed or released
m is the mass of the substance
c is the specific heat of the substance
ΔT is the change in temperature

In this case, the metal was placed in boiling water until it reached the temperature of the water. This means that the final temperature of the metal is 96.0oC.

The heat absorbed by the metal is calculated as follows:

q = mcΔT

Where:
m = mass of the metal
c = specific heat of the metal
ΔT = change in temperature of the metal

First, we need to find the value of q, the heat absorbed by the metal. From the information given, we know that the heat absorbed by the foam cup is 42.0 J/oC, and the temperature of the water in the foam cup increased from 20.0oC to 24.0oC.

The heat absorbed by the water in the foam cup is calculated as follows:

q = mcΔT

Where:
m = mass of water
c = specific heat of water
ΔT = change in temperature of water

Given:
m (mass of water) = 50.0 g
c (specific heat of water) = 4.18 J/g·°C (specific heat of water is commonly approximated as 4.18 J/g·°C)
ΔT (change in temperature of water) = 24.0oC - 20.0oC = 4.0oC

Substituting the given values into the formula, we get:

q = (50.0 g) × (4.18 J/g·°C) × (4.0oC)

q = 836 J

Now we know that the heat absorbed by the metal is 836 J. We also know that the mass of the metal is 36.7 g, and the change in temperature of the metal is:

ΔT = 96.0oC - 24.0oC = 72.0oC

Substituting the known values into the formula, we get:

836 J = (36.7 g) × c × (72.0oC)

To find the specific heat of the metal (c), rearrange the equation:

c = 836 J / [(36.7 g) × (72.0oC)]

Calculating this expression will give you the specific heat of the metal.