A block of copper at 100 degrees Celsius comes in contact with a block of aluminum at 20 degrees Celsius. The final temp of the blocks is 60 degrees Celsius. What are the relative masses of the blocks?

[mass Cu x specific heat Cu x (60-100)] + [mass Al x specific heat Al x (60-20)] = 0

You must look up the specific heat for the two metals, plug those into the equation and solve for mass Cu/mass Al.

To solve this problem, we can use the principle of energy conservation, specifically the principle of heat transfer.

The equation for heat transfer between two objects is given by:

q = m * c * ΔT

Where:
q is the amount of heat transferred
m is the mass of the object
c is the specific heat capacity of the material
ΔT is the change in temperature

Since the final temperature is 60°C, we can calculate the change in temperature for each object.

For the copper block:
ΔTcopper = Final temperature - Initial temperature = 60°C - 100°C = -40°C

For the aluminum block:
ΔTaluminum = Final temperature - Initial temperature = 60°C - 20°C = 40°C

Next, let's assume the mass of the copper block is mcopper and the mass of the aluminum block is maluminum. We need to find the ratio of their masses.

According to the principle of heat transfer:

q(copper) = -q(aluminum)

Using the equation for heat transfer, we can write:

mcopper * ccopper * ΔTcopper = -maluminum * caluminum * ΔTaluminum

Since the specific heat capacities for copper (ccopper) and aluminum (caluminum) are constant, we can rewrite the equation as:

mcopper * ΔTcopper = -maluminum * ΔTaluminum

Substituting the values we calculated earlier:

mcopper * (-40)°C = -maluminum * 40°C

Dividing both sides by -40°C:

mcopper = maluminum * (40/(-40))

Simplifying:

mcopper = -maluminum

mcopper/maluminum = -1

From the equation, we can conclude that the mass of the copper block is equal to the negative of the mass of the aluminum block. As a result, we cannot determine the exact relative masses of the blocks with the information given.

To find the relative masses of the copper and aluminum blocks, we can use the concept of heat transfer and the principle of conservation of energy.

The heat lost by the copper block is equal to the heat gained by the aluminum block. The equation for heat transfer is given by:

Q = mcΔT

where Q is the heat transfer, m is the mass, c is the specific heat capacity of the material, and ΔT is the change in temperature.

For the copper block, the initial temperature (Ti) is 100 degrees Celsius, and the final temperature (Tf) after coming in contact with the aluminum block is 60 degrees Celsius. Therefore, the change in temperature (ΔTcopper) is given by:

ΔTcopper = Tf - Ti = 60 - 100 = -40 degrees Celsius

Similarly, for the aluminum block, the initial temperature (Ti) is 20 degrees Celsius, and the final temperature (Tf) after coming in contact with the copper block is 60 degrees Celsius. The change in temperature (ΔTaluminum) is given by:

ΔTaluminum = Tf - Ti = 60 - 20 = 40 degrees Celsius

Since the heat lost by the copper block is equal to the heat gained by the aluminum block, we can set up the equation:

mcopper * c(copper) * ΔTcopper = maluminum * c(aluminum) * ΔTaluminum

Dividing both sides by c(copper) * ΔTcopper and rearranging the equation, we get:

mcopper / maluminum = c(aluminum) * ΔTaluminum / c(copper) * ΔTcopper

Now, we can substitute the known values for specific heat capacities and temperature differences:

mcopper / maluminum = c(aluminum) * 40 / c(copper) * (-40)

By plugging in the specific heat capacities for aluminum and copper, we can determine the relative masses of the blocks:

mcopper / maluminum = (0.897 * 40) / (0.387 * (-40))

Performing the calculations:

mcopper / maluminum = 35.88 / -15.48

mcopper / maluminum ≈ -2.32

The relative masses of the blocks are approximately 2.32. The negative sign indicates that the mass of the copper block is negative relative to the mass of the aluminum block, which is not physically meaningful. Therefore, we can consider the relative masses to be approximately 1:2.32, with the aluminum block being larger in mass.