Spaceman Spiff sits just outside the Milky Way galaxy with a cup of liquid Helium which is at approximately 4K (-269 0C). He has with him a small sphere made entirely of copper which is at a temperature of 219K (-54 0C). After a certain amount of time his copper sphere comes into equilibrium with the liquid Helium. If his sphere has a diameter of 2 cm, a mass density of 8.96 g/cm3, and a specific heat of 0.386 J * K-1 * g-1, and the process of the copper coming into equilibrium with the liquid helium burned off 150g of liquid Helium, what is the latent heat of vaporization of liquid Helium? (assume that 4K is the boiling point of He and there is more than 150g of He)
To determine the latent heat of vaporization of liquid helium, we need to consider the heat transfer that occurs when the copper sphere reaches equilibrium with the liquid helium.
First, let's calculate the mass of the copper sphere. We can use the formula for the volume of a sphere:
Volume = (4/3) * π * r^3
Given that the diameter of the sphere is 2 cm, the radius (r) can be calculated as half of the diameter:
r = 2 cm / 2 = 1 cm = 0.01 m
Now we can calculate the volume:
Volume = (4/3) * π * (0.01 m)^3 ≈ 4.19 x 10^-6 m^3
The mass of the copper sphere can be calculated using the mass density:
Mass = Density * Volume
Given that the density of copper is 8.96 g/cm^3, converting it to kg/m^3:
Density = 8.96 g/cm^3 * (1000 kg/m^3 / 1 g/cm^3) = 8960 kg/m^3
Mass = 8960 kg/m^3 * 4.19 x 10^-6 m^3 ≈ 0.0375 kg
Next, let's calculate the change in temperature ΔT of the copper sphere to reach equilibrium with the liquid helium:
ΔT = 219 K - 4 K = 215 K
The heat transferred from the copper sphere to the liquid helium can be calculated using the formula:
Heat = Mass * Specific Heat * ΔT
Given that the specific heat of copper is 0.386 J * K^-1 * g^-1, converting it to J * K^-1 * kg^-1:
Specific Heat = 0.386 J * K^-1 * g^-1 * (1 kg / 1000 g) = 0.386 J * K^-1 * kg^-1
Heat = 0.0375 kg * 0.386 J * K^-1 * kg^-1 * 215 K ≈ 3.31 J
Since 150 g of liquid helium is burned off during the process of equilibrium, the heat transferred is equal to the latent heat of vaporization (Q):
Q = 150 g * Latent Heat of Vaporization
Therefore:
Latent Heat of Vaporization = Q / (150 g)
Substituting the previously calculated value of Q:
Latent Heat of Vaporization = 3.31 J / (150 g) ≈ 0.022 J/g
Therefore, the latent heat of vaporization of liquid helium is approximately 0.022 J/g.
To find the latent heat of vaporization of liquid Helium, we need to calculate the amount of heat transferred from the liquid Helium to the copper sphere during the process of reaching equilibrium.
First, let's calculate the mass of the copper sphere. The mass can be calculated using the formula:
Mass = Density * Volume
Given that the diameter of the copper sphere is 2 cm, we can find its radius (r) by dividing the diameter by 2:
r = 2 cm / 2 = 1 cm = 0.01 m
The volume of the sphere can be calculated using the formula:
Volume = (4/3) * π * r^3
Volume = (4/3) * π * (0.01 m)^3
Next, let's calculate the mass of the copper sphere using its density:
Density = 8.96 g/cm^3
Mass = Density * Volume
Now that we have the mass of the copper sphere, we can calculate the heat transferred to it during the process of reaching equilibrium. The formula to calculate heat transfer is:
Heat Transfer = mass * specific heat * change in temperature
Given that the initial temperature of the copper sphere is 219 K (-54 °C), and the final temperature is 4 K, we can calculate the change in temperature.
Change in temperature = 4 K - 219 K
Finally, we can find the latent heat of vaporization (L) using the formula:
L = Heat Transfer / Mass of He
where the Heat Transfer is the heat transferred to the copper sphere, and the Mass of He is the amount of liquid Helium consumed during the process.
Now let's substitute the calculated values into the formulas to find the answer!