Calculate how much work does a block of aluminum of mass 100 kg do if it is heated at P = 1 atm from 20 degrees to 660 degrees.
n.b. - The density of solid aluminum at 20 degrees is p= 2.7 g/cm^3. When it
is liquid at 660^C the density of the liquid state is decreased to
2.38 g/cm3.
To calculate the work done by the block of aluminum when heated, we need to consider the change in volume of the aluminum.
Step 1: Calculate the initial volume of the aluminum block.
Given the mass of the aluminum block, m = 100 kg, and the density of solid aluminum at 20 degrees, ρ = 2.7 g/cm^3, we can calculate the initial volume using the formula:
V_initial = m / ρ
First, convert the mass to grams:
m = 100 kg * 1000 g/kg = 100,000 g
Now, substitute the values into the formula and calculate:
V_initial = 100,000 g / 2.7 g/cm^3 = 37,037 cm^3
Step 2: Calculate the final volume of the aluminum block.
Given the density of aluminum in its liquid state at 660 degrees, ρ = 2.38 g/cm^3, we can calculate the final volume using the formula:
V_final = m / ρ
Substitute the values and calculate:
V_final = 100,000 g / 2.38 g/cm^3 = 42,017 cm^3
Step 3: Calculate the change in volume.
ΔV = V_final - V_initial
Substitute the values and calculate:
ΔV = 42,017 cm^3 - 37,037 cm^3 = 4,980 cm^3
Step 4: Calculate the work done.
The work done by the block of aluminum is given by the formula:
Work = Pressure * ΔV
Given that the pressure is constant at P = 1 atm and ΔV = 4,980 cm^3, we can calculate the work:
Work = 1 atm * 4,980 cm^3 = 4,980 atm.cm^3
Note: Since we need to express the work in a standard SI unit (Joules), we need to convert atm.cm^3 to Joules.
1 atm.cm^3 = 101.325 J
Final calculation:
Work = 4,980 atm.cm^3 * 101.325 J/atm.cm^3 = 504,261.9 J
Therefore, the block of aluminum does approximately 504,262 Joules of work when heated from 20 degrees to 660 degrees under a pressure of 1 atm.