A piece of copper metal (specific heat 0.385 J/g∘C) at 85.6 ∘C is placed in 50.0 g of water at 16.2 ∘C. The metal and water come to the same temperature of 23.6 ∘C. What is the mass?

I assume you are asking for the mass of the Cu since you already have the mass of the water.

[mass Cu x specific heat Cu x (Tfinal-Tinitial)] + [mass H2O x specific heat H2o x (Tfinal-Tinitial)] = 0
Substitute the numbers and solve for mass Cu metal.

To find the mass of the copper metal, we can use the equation for heat transfer:

q = mcΔT

Where:
q = heat transfer
m = mass
c = specific heat
ΔT = change in temperature

First, let's calculate the heat transfer for the copper metal:

q1 = mcΔT1

q1 = (mass of copper)(specific heat of copper)(final temperature - initial temperature)

We know the specific heat of copper is 0.385 J/g∘C, the initial temperature is 85.6 ∘C, and the final temperature is 23.6 ∘C. However, we do not know the mass of the copper, so let's call it 'm':

q1 = m(0.385 J/g∘C)(23.6 ∘C - 85.6 ∘C)

Next, let's calculate the heat transfer for the water using the same equation:

q2 = mcΔT2

q2 = (mass of water)(specific heat of water)(final temperature - initial temperature)

We know the mass of the water is 50.0 g and the specific heat of water is 4.18 J/g∘C. The initial temperature is 16.2 ∘C, and the final temperature is also 23.6 ∘C:

q2 = (50.0 g)(4.18 J/g∘C)(23.6 ∘C - 16.2 ∘C)

According to the law of conservation of energy, the heat lost by the copper is equal to the heat gained by the water. Therefore:

q1 = q2

m(0.385 J/g∘C)(23.6 ∘C - 85.6 ∘C) = (50.0 g)(4.18 J/g∘C)(23.6 ∘C - 16.2 ∘C)

Now we can solve for the mass 'm' of the copper metal.

To find the mass of the copper metal, we can use the principle of heat exchange:

The heat lost by the copper metal = heat gained by the water

The formula for heat exchange is:

q = m * c * ΔT

Where:
q is the heat exchanged,
m is the mass,
c is the specific heat, and
ΔT is the change in temperature.

In this case, the heat lost by the copper metal is equal to the heat gained by the water. We can set up the equation as follows:

(metal mass) * (copper specific heat) * (final temperature - initial temperature of the copper) = (water mass) * (water specific heat) * (final temperature - initial temperature of the water)

We know the initial and final temperatures of both the copper and the water, the specific heat of copper, and the mass of the water. We need to find the mass of the copper metal.

Let's plug in the values:

(metal mass) * (0.385 J/g∘C) * (23.6 ∘C - 85.6 ∘C) = (50.0 g) * (4.18 J/g∘C) * (23.6 ∘C - 16.2 ∘C)

Simplifying the equation gives:

(metal mass) * (-62 ∘C) * (0.385 J/g∘C) = (50.0 g) * (4.18 J/g∘C) * (7.4 ∘C)

Using algebra, we can solve for the metal mass:

(metal mass) = (50.0 g) * (4.18 J/g∘C) * (7.4 ∘C) / (62 ∘C * 0.385 J/g∘C)

Calculating the values gives:

(metal mass) ≈ 54.03 g

Therefore, the mass of the copper metal is approximately 54.03 grams.

use the formula q = m*c*deltaT