How much heat energy must be added to a 3.0 cm × 3.0 cm × 3.0 cm block of aluminum to raise its temperature from -50∘C to 50∘C?

volume=27cm^3

look up density of aluminum
look up specific heat aluminum (J/cm^3 K)

heatenergy=density*volume*specifHeat*(changeinTemp)
change in temp=100C

To determine the heat energy required to raise the temperature of a substance, we can use the formula:

Q = mcΔT

Where:
Q is the heat energy (in joules)
m is the mass of the substance (in kilograms)
c is the specific heat capacity of the substance (in joules per kilogram per degree Celsius)
ΔT is the change in temperature (in degrees Celsius)

To apply this formula to your question, we first need to calculate the mass of the aluminum block. We'll assume that the density of aluminum is approximately 2.7 g/cm³.

The volume of the block can be calculated using the formula:

V = l × w × h

Where:
V is the volume
l, w, and h are the length, width, and height of the block

Given the dimensions of the block as 3.0 cm × 3.0 cm × 3.0 cm, we can substitute these values into the formula to find the volume.

V = 3.0 cm × 3.0 cm × 3.0 cm

Next, we need to convert the volume from cubic centimeters to cubic meters since the density of aluminum is given in kilograms per cubic meter.

1 cubic meter is equal to 1,000,000 cubic centimeters. Therefore, we divide the volume by 1,000,000 to get the volume in cubic meters.

Now that we have the volume in cubic meters, we can calculate the mass of the aluminum block using the formula:

mass = density × volume

Substituting the values, we get:

mass = 2.7 g/cm³ × (volume in cubic meters) kg/m³

Once we have the mass, we need to find the specific heat capacity of aluminum. The specific heat capacity of aluminum is approximately 900 J/kg°C.

Finally, we can substitute all the values into the heat energy formula:

Q = mcΔT

Where:
m = mass of the aluminum block
c = specific heat capacity of aluminum
ΔT = change in temperature (from -50°C to 50°C)

By following these steps and performing the calculations, we can determine the amount of heat energy required.