The latent heat of fusion of alcohol is 50 kcal/kg and its melting point is -54oC. It has a specific heat of 0.60 in its liquid state. Calculate the energy needed to melt 2.0 kg of solid alcohol at -54o and raise it to a temperature of -4°C.
170 kJ
To calculate the energy needed, we need to consider two steps:
Step 1: The energy required to melt the solid alcohol at its melting point.
Step 2: The energy required to raise the temperature of the liquid alcohol from -54°C to -4°C.
Step 1: The energy needed to melt the solid alcohol can be calculated using the formula:
Energy = mass × latent heat of fusion
Given:
Mass of solid alcohol = 2.0 kg
Latent heat of fusion = 50 kcal/kg
Energy = 2.0 kg × 50 kcal/kg
Energy = 100 kcal
Step 2: The energy needed to raise the temperature of the liquid alcohol from -54°C to -4°C can be calculated using the formula:
Energy = mass × specific heat × change in temperature
Given:
Mass of liquid alcohol = 2.0 kg
Specific heat = 0.60
Change in temperature = (-4°C) - (-54°C) = 50°C
Energy = 2.0 kg × 0.60 × 50°C
Energy = 60 kcal
Therefore, the total energy needed to melt 2.0 kg of solid alcohol at -54°C and raise it to a temperature of -4°C is 100 kcal + 60 kcal = 160 kcal.
To calculate the energy needed to melt 2.0 kg of solid alcohol at -54°C and raise it to a temperature of -4°C, we can break down the problem into two parts: the energy to melt the solid alcohol and the energy to raise the temperature from -54°C to -4°C.
1. Calculating the energy needed to melt the solid alcohol:
The energy needed to melt a substance can be calculated using the formula:
Energy = mass * latent heat of fusion
Given: mass = 2.0 kg and latent heat of fusion = 50 kcal/kg
Energy = 2.0 kg * 50 kcal/kg
Energy = 100 kcal
So, the energy needed to melt the solid alcohol is 100 kcal.
2. Calculating the energy needed to raise the temperature from -54°C to -4°C:
The energy needed to raise the temperature of a substance can be calculated using the formula:
Energy = mass * specific heat * temperature change
Given: mass = 2.0 kg, specific heat = 0.60, temperature change = -4°C - (-54°C) = 50°C
Energy = 2.0 kg * 0.60 * 50°C
Energy = 60 kcal
So, the energy needed to raise the temperature of the liquid alcohol from -54°C to -4°C is 60 kcal.
Therefore, the total energy needed to melt 2.0 kg of solid alcohol at -54°C and raise it to a temperature of -4°C is:
Total Energy = Energy to melt + Energy to raise temperature
Total Energy = 100 kcal + 60 kcal
Total Energy = 160 kcal
Hence, the energy needed is 160 kcal.