Calculate the amount of energy in calories that is needed to melt 45g of ice at -20°C and then increase the temperature to 95°C
q for ice at -20 to ice at 0.
q = mass x specific heat ice x delta T (dT = 20).
q to melt the ice is
q = mass ice x heat fusion.
q to heat from zero to 95.
q = mass H2O x specific heat H2O x dT and dT = 95.
Then sum the q values.
To calculate the amount of energy needed to melt the ice and subsequently increase the temperature, we need to consider two separate processes: the heat required for the phase change (melting) and the heat required to raise the temperature.
1. Heat required to melt the ice:
The heat required for melting can be calculated using the formula:
Q = m * Lf
where Q is the heat energy needed, m is the mass of the ice, and Lf is the latent heat of fusion.
The latent heat of fusion of ice is approximately 334 J/g.
For our calculation:
m = 45g
Lf = 334 J/g
Q = 45g * 334 J/g = 15030 J
Converting this value to calories:
1 calorie (cal) = 4.184 J
Q = 15030 J * (1 cal / 4.184 J) = 3591.24 cal
Therefore, approximately 3591.24 calories of energy are required to melt 45g of ice.
2. Heat required to increase the temperature:
The heat required to raise the temperature of a substance can be calculated using the formula:
Q = m * C * ΔT
where Q is the heat energy needed, m is the mass of the substance, C is the specific heat capacity, and ΔT is the change in temperature.
The specific heat capacity of water is approximately 4.18 J/g°C.
For our calculation, let's consider the water after melting the ice:
m = 45g
C = 4.18 J/g°C
ΔT = 95°C - 0°C = 95°C
Q = 45g * 4.18 J/g°C * 95°C = 18113.5 J
Converting this value to calories:
Q = 18113.5 J * (1 cal / 4.184 J) = 4332.33 cal
Therefore, approximately 4332.33 calories of energy are required to raise the temperature of the water from 0°C to 95°C.
Adding the results of both steps together:
Total energy = heat for phase change + heat for temperature increase
= 3591.24 cal + 4332.33 cal
≈ 7923.57 cal
Therefore, approximately 7923.57 calories of energy are needed to melt 45g of ice at -20°C and then increase the temperature to 95°C.
To calculate the amount of energy required to melt the ice and then increase its temperature, we need to consider two separate processes: the energy required for the phase change (melting) and the energy required to raise the temperature.
First, let's calculate the energy needed to melt the ice:
The heat required to melt a solid substance can be determined using the equation:
Q = m * ΔH_fusion
where:
Q is the heat energy required,
m is the mass of the substance, and
ΔH_fusion is the heat of fusion (amount of energy needed to change the substance from solid to liquid) for the specific substance.
The heat of fusion for ice is usually given as 333.55 J/g.
To convert grams to kilograms, divide the mass by 1000:
m = 45 g / 1000 = 0.045 kg
Now we can calculate the heat energy required for phase change:
Q_fusion = m * ΔH_fusion
= 0.045 kg * 333.55 J/g
= 14.86 kJ
Next, let's calculate the energy required to raise the temperature of the liquid water from -20°C to 0°C:
The heat required to change the temperature of a substance can be calculated using the equation:
Q = m * c * ΔT
where:
Q is the heat energy required,
m is the mass of the substance,
c is the specific heat capacity of the substance, and
ΔT is the change in temperature.
The specific heat capacity of water is around 4.18 J/g°C.
ΔT = 0°C - (-20°C) = 20°C
Now we can calculate the heat energy required to raise the temperature:
Q_temp_increase = m * c * ΔT
= 0.045 kg * 4.18 J/g°C * 20°C
= 3.78 kJ
Finally, let's calculate the energy required to raise the temperature of the water from 0°C to 95°C:
ΔT = 95°C - 0°C = 95°C
Q_temp_increase = m * c * ΔT
= 0.045 kg * 4.18 J/g°C * 95°C
= 17.89 kJ
To find the total energy, we add up the energy required for each step:
Total energy = Q_fusion + Q_temp_increase + Q_temp_increase
= 14.86 kJ + 3.78 kJ + 17.89 kJ
≈ 36.53 kJ
Now we can convert the energy from joules to calories:
1 calorie (cal) = 4.184 joules (J)
So,
Total energy in calories = 36.53 kJ * 1000 cal/kJ / 4.184 J
≈ 8733 cal
Therefore, the amount of energy needed to melt 45g of ice at -20°C and then increase the temperature to 95°C is approximately 8733 calories.