Please help
how much heat is needed to transform a 2.5 kg block of ice at -4°c to a puddle of water at 12°c? Cwater=4200J kg^-1 °C^-1, Cice=2100J kg^-1 °C^-1, Lf=3.33*10^5 J kg^-1.
To find the amount of heat needed to transform a block of ice into water, we need to consider two parts: first, we need to heat the ice from -4°C to 0°C, and then we need to melt the ice at 0°C into water at 0°C, and finally, we need to heat the water from 0°C to 12°C.
Let's break down the steps:
1. Heating the ice from -4°C to 0°C:
The specific heat capacity of ice (Cice) is given as 2100 J kg^-1 °C^-1. We can use the formula:
Q1 = m * Cice * ΔT1
Where:
Q1 is the heat energy required,
m is the mass of the ice (2.5 kg),
Cice is the specific heat capacity of ice (2100 J kg^-1 °C^-1), and
ΔT1 is the change in temperature (0°C - (-4°C) = 4°C).
So, substituting the values:
Q1 = 2.5 kg * 2100 J kg^-1 °C^-1 * 4°C
Q1 = 21,000 J
Therefore, it takes 21,000 Joules of heat energy to heat the ice from -4°C to 0°C.
2. Melting the ice at 0°C into water at 0°C:
The latent heat of fusion (Lf) for ice is given as 3.33 * 10^5 J kg^-1. Since we have 2.5 kg of ice, we can use the formula:
Q2 = m * Lf
Where:
Q2 is the heat energy required,
m is the mass of the ice (2.5 kg),
Lf is the latent heat of fusion (3.33 * 10^5 J kg^-1).
So, substituting the values:
Q2 = 2.5 kg * 3.33 * 10^5 J kg^-1
Q2 = 8.325 * 10^5 J
Therefore, it takes 8.325 * 10^5 Joules of heat energy to melt the ice into water.
3. Heating the water from 0°C to 12°C:
The specific heat capacity of water (Cwater) is given as 4200 J kg^-1 °C^-1. We can use the formula:
Q3 = m * Cwater * ΔT3
Where:
Q3 is the heat energy required,
m is the mass of the water (which is the same as the mass of ice, 2.5 kg),
Cwater is the specific heat capacity of water (4200 J kg^-1 °C^-1), and
ΔT3 is the change in temperature (12°C - 0°C = 12°C).
So, substituting the values:
Q3 = 2.5 kg * 4200 J kg^-1 °C^-1 * 12°C
Q3 = 126,000 J
Therefore, it takes 126,000 Joules of heat energy to heat the water from 0°C to 12°C.
Adding all the heat energies together:
Total heat energy = Q1 + Q2 + Q3
Total heat energy = 21,000 J + 8.325 * 10^5 J + 126,000 J
Total heat energy = 9.47125 * 10^5 J
So, it takes approximately 947,125 Joules of heat energy to transform a 2.5 kg block of ice at -4°C into a puddle of water at 12°C.