Suppose you are camping in the mountains and you need to melt 1.8 kg of snow at 0.0 degC to 70.0 degC. The specific heat of water is 4186 j/kg*C while the latent heat of fusion for water equals 3.34 x 10^5 J/kg.
How much heat will be needed?
Express in KJ.
To determine the amount of heat needed to melt and heat up the snow, we need to consider two steps: melting the snow and heating the resulting water.
Step 1: Melting the snow
The amount of heat required to melt the snow can be calculated using the formula:
Q1 = mass * latent heat of fusion
Given:
mass = 1.8 kg
latent heat of fusion = 3.34 x 10^5 J/kg
Substituting the values into the formula gives us:
Q1 = 1.8 kg * 3.34 x 10^5 J/kg
Calculating Q1, we find:
Q1 = 6.012 x 10^5 J
Step 2: Heating the water
The specific heat capacity of water is required to calculate the heat needed to heat up the resulting water. The specific heat capacity of water is:
C = 4186 J/kg*C
To determine the heat required to raise the temperature of the water from 0.0°C to 70.0°C, we can use the formula:
Q2 = mass * specific heat capacity * change in temperature
Given:
mass = 1.8 kg
specific heat capacity = 4186 J/kg*C
change in temperature = 70.0°C - 0.0°C = 70.0°C
Substituting the values into the formula gives us:
Q2 = 1.8 kg * 4186 J/kg*C * 70.0°C
Calculating Q2, we find:
Q2 = 5.85728 x 10^5 J
Total heat required:
The total heat required is the sum of Q1 and Q2:
Total heat = Q1 + Q2
Substituting the values, we find:
Total heat = 6.012 x 10^5 J + 5.85728 x 10^5 J
Calculating the total heat in kilojoules (kJ), we divide the result by 1000:
Total heat = (6.012 x 10^5 J + 5.85728 x 10^5 J) / 1000 kJ
Total heat = 1186.528 kJ