A puddle filled with 20. kg of water is completely frozen to -6.0 degrees celcius in the middle of winter. How much heat must be absorbed by the puddle to melt the ice and warm the water up to 20. celcius during the spring thaw?
20 kg [ specific heat of ice in cals or joules /kg deg * 6 + heat of fusion of water + specific heat of water * 20 ]=answer in calories or Joules
20(2090)(20+6)=1086800 J
8625600 Joules
To calculate the amount of heat required to melt the ice and warm the water, we need to consider two separate processes: first, melting the ice, and second, heating the water.
1. Melting the ice:
The heat required to melt the ice can be calculated using the formula:
Q1 = m * Lf
where Q1 is the heat absorbed, m is the mass of the ice, and Lf is the specific latent heat of fusion for ice.
Given:
m = 20. kg (mass of ice)
Lf = 334,000 J/kg (specific latent heat of fusion for ice)
Substituting the values into the formula, we get:
Q1 = (20. kg) * (334,000 J/kg)
Q1 ≈ 6,680,000 J
Therefore, it would take approximately 6,680,000 J of heat to melt the ice completely.
2. Heating the water:
The heat required to raise the temperature of the water can be calculated using the formula:
Q2 = m * Cp * ΔT
where Q2 is the heat absorbed, m is the mass of the water, Cp is the specific heat capacity of water, and ΔT is the change in temperature.
Given:
m = 20. kg (mass of water)
Cp = 4,186 J/kg°C (specific heat capacity of water)
ΔT = (20. °C - (-6.0 °C)) = 26.0 °C (change in temperature)
Substituting the values into the formula, we get:
Q2 = (20. kg) * (4,186 J/kg°C) * (26.0 °C)
Q2 ≈ 2,725,520 J
Therefore, it would take approximately 2,725,520 J of heat to raise the temperature of the water from -6.0 °C to 20.0 °C.
To find the total heat required, we add the heat required to melt the ice (Q1) and the heat required to warm the water (Q2):
Total heat = Q1 + Q2
Total heat ≈ 6,680,000 J + 2,725,520 J
Total heat ≈ 9,405,520 J
Therefore, approximately 9,405,520 J of heat must be absorbed by the puddle to melt the ice completely and warm the water up to 20.0 °C.