Aluminum is melted during the recycling process.

(a) How much heat must be transferred to each kilogram of aluminum to bring it to its melting point, 660 degrees C, from room temperature, 20 degrees C?
(b) About how many cups of coffee could you make with this much heat?

heat=mass*specificheatAL*(660-25)

To calculate the heat required to bring aluminum to its melting point, we need to use the formula:

Q = mcΔT

Where:
Q = Heat (in Joules)
m = Mass of aluminum (in kg)
c = Specific heat capacity of aluminum (in J/kg·°C)
ΔT = Change in temperature (in °C)

(a) Let's calculate the heat required:

Mass of aluminum: 1 kg
Specific heat capacity of aluminum: 897 J/kg·°C
Change in temperature: 660°C - 20°C = 640°C

Q = 1 kg * 897 J/kg·°C * 640°C
Q = 575,680 J

Therefore, the amount of heat required to melt 1 kg of aluminum is 575,680 J.

(b) Now, let's determine how many cups of coffee can be made with this amount of heat.

According to a rough estimation, it takes approximately 500,000 J of heat to heat a cup (250 mL) of water from room temperature to boiling (assumed to be 100°C).

So, the number of cups of coffee can be calculated by dividing the total heat (Q) by the heat required to heat one cup of water:

Number of cups = Q / heat required for one cup

Number of cups = 575,680 J / 500,000 J
Number of cups ≈ 1.15 cups

Therefore, with the heat required to melt 1 kg of aluminum, approximately 1.15 cups of coffee can be made.

To determine the amount of heat required to raise the temperature of aluminum from 20°C to 660°C, we need to use the specific heat capacity of aluminum. The specific heat capacity denotes the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius per unit mass.

(a) To calculate the heat transfer for each kilogram of aluminum, we can use the formula:

Q = m * c * ΔT

Where:
Q = Heat transfer (in joules)
m = Mass of aluminum (in kilograms)
c = Specific heat capacity of aluminum
ΔT = Change in temperature (in degrees Celsius)

The specific heat capacity of aluminum is approximately 900 J/kg°C. Thus, we can substitute the values into the formula:

ΔT = 660°C - 20°C = 640°C

Q = 1 kg * 900 J/kg°C * 640°C = 576,000 J

Therefore, it would require 576,000 joules of heat energy to melt 1 kilogram of aluminum from room temperature to its melting point.

(b) Converting the heat energy into the number of cups of coffee can be achieved by considering the energy required to heat a cup of water. Let's assume you use an average-sized cup of water, which is approximately 240 milliliters (ml), and you want to increase the temperature of the water by 80°C.

The specific heat capacity of water is roughly 4.18 J/g°C, and considering that 1 ml of water weighs approximately 1 gram, we can calculate the heat energy required to heat a cup of water:

Q = m * c * ΔT

Where:
Q = Heat transfer (in joules)
m = Mass of water (in grams)
c = Specific heat capacity of water
ΔT = Change in temperature (in degrees Celsius)

Q = 240 g * 4.18 J/g°C * 80°C = 79,872 J

Now, we can calculate the number of cups of coffee that can be made from the heat energy required to melt 1 kilogram of aluminum:

Cups of coffee = Heat energy required to melt aluminum / Heat energy per cup of coffee

Cups of coffee = 576,000 J / 79,872 J ≈ 7.21 cups

Therefore, approximately 7 cups of coffee could be made with the amount of heat energy required to melt 1 kilogram of aluminum.