Part A: Find the amount of heat that must be extracted from 1.5 kg of steam at 130 ∘C to convert it to ice at 0.0 ∘C.
Part B: What speed would this 1.5-kg block of ice have if its translational kinetic energy were equal to the thermal energy calculated in part A?
someone help me out
Part A:
To find the amount of heat that must be extracted from the steam to convert it to ice, we can use the equation:
Q = m * L
where:
Q is the amount of heat transferred,
m is the mass of the substance, and
L is the specific latent heat.
For steam at 130 °C, we need to use the specific latent heat of vaporization (Lv).
First, let's calculate the amount of heat required to convert the steam to water at 100 °C, using the specific latent heat of vaporization (Lv) for steam:
Q1 = m * Lv
Next, let's calculate the amount of heat required to cool the water from 100 °C to 0 °C, using the specific heat capacity (C) for water:
Q2 = m * C * ΔT
where:
C is the specific heat capacity of water, and
ΔT is the change in temperature.
Finally, we can add Q1 and Q2 to get the total amount of heat required:
Q_total = Q1 + Q2
Part B:
To determine the speed of the block of ice, we can use the equation for translational kinetic energy:
KE = 0.5 * m * v^2
where:
KE is the kinetic energy,
m is the mass of the object, and
v is the velocity.
We can equate the thermal energy calculated in part A (Q_total) to the kinetic energy (KE) and solve for v:
Q_total = KE
Now, substitute the calculated Q_total value into the equation and solve for v:
Q_total = 0.5 * m * v^2
v^2 = (2 * Q_total) / m
v = √[(2 * Q_total) / m]
Substitute the values obtained in part A into this equation to get the speed of the block of ice.