Calculate the amount of heat (joules) required to convert 200 g of ice cubes (00 C) to gas at 100 0 (10 pts)
q1 to convert convert ice at zero C to liquid.
q1 = mass ice x heat fusion = ?
q2 to heat water @ zero C to 100 C.
q2 = mass water x specific heat liquid H2O x (Tfinal-Tinitial). Tfnial is 100 and Tinitial is zero
q3 to convert liquid H2O to steam.
q3 = mass H2O x heat vaporization.
QTotal = q1 + q2 + q3
Post your work if you get stuck.
joules) required to convert 200 g of ice cubes (0 ° Celsius) to gas at 100° Celsius.
To determine the amount of heat required to convert 200 g of ice cubes from 0°C to gas at 100°C, we need to calculate the heat required for each phase change individually and then sum them up.
First, let's calculate the heat required to raise the temperature of the ice cubes from 0°C to water at 0°C. For this step, we will use the specific heat capacity of ice, which is 2.09 J/g°C.
The formula to calculate the heat for this step is:
Q = m * c * ΔT,
where Q is the heat (joules), m is the mass (grams), c is the specific heat capacity (joules/gram°C), and ΔT is the change in temperature (°C).
Using this formula:
Q1 = 200 g * 2.09 J/g°C * (0°C - 0°C)
Q1 = 0 Joules
Next, let's calculate the heat required to convert the ice at 0°C to water at 0°C. This step is known as the latent heat of fusion, and it represents the heat absorbed during the phase change.
The latent heat of fusion for ice is 334,000 J/kg.
To convert this value to grams, we divide it by 1000 (1 kg = 1000 g):
latent heat of fusion (L) = 334,000 J/kg = 334 J/g
Using this value, the formula to calculate the heat for this step is:
Q2 = m * L,
where Q2 is the heat (joules), m is the mass (grams), and L is the latent heat of fusion (joules/gram).
Q2 = 200 g * 334 J/g
Q2 = 66,800 Joules
Finally, let's calculate the heat required to convert the water at 0°C to gas at 100°C. This step is known as the latent heat of vaporization, and it represents the heat absorbed during the phase change.
The latent heat of vaporization for water is 2,260,000 J/kg.
Similarly to the previous step, let's convert this value to grams:
latent heat of vaporization (L) = 2,260,000 J/kg = 2,260 J/g
Using this value, the formula to calculate the heat for this step is:
Q3 = m * L,
where Q3 is the heat (joules), m is the mass (grams), and L is the latent heat of vaporization (joules/gram).
Q3 = 200 g * 2,260 J/g
Q3 = 452,000 Joules
Finally, we sum up the three steps to find the total heat required:
Total heat (Q_total) = Q1 + Q2 + Q3
Total heat (Q_total) = 0 Joules + 66,800 Joules + 452,000 Joules
Total heat (Q_total) = 518,800 Joules
Therefore, the amount of heat required to convert 200 g of ice cubes from 0°C to gas at 100°C is 518,800 Joules.
To calculate the amount of heat required to convert 200g of ice cubes from 0°C to gas at 100°C, we need to consider three stages:
1. Heating the ice from -2°C (since the ice cube temperature is usually slightly below 0°C) to 0°C.
2. Melting the ice at 0°C.
3. Heating the liquid water from 0°C to 100°C, then vaporizing it at 100°C.
To calculate the amount of heat required for each stage, we need to use the specific heat capacity and heat of fusion/evaporation values.
1. Heating the ice from -2°C to 0°C:
The specific heat capacity (c) of ice is 2.09 J/g°C.
The formula to calculate the heat (q) required is q = mcΔT, where m is the mass (200g), c is the specific heat capacity, and ΔT is the change in temperature.
q1 = (200g) * (2.09 J/g°C) * (0 - (-2)°C)
q1 = (200g) * (2.09 J/g°C) * (2°C)
q1 = 836 J
2. Melting the ice at 0°C:
The heat of fusion (Hf) for ice is 334 J/g.
The formula to calculate the heat (q) required is q = mHf, where m is the mass (200g).
q2 = (200g) * (334 J/g)
q2 = 66,800 J
3. Heating the liquid water from 0°C to 100°C and vaporizing it at 100°C:
The specific heat capacity of liquid water is 4.18 J/g°C.
The heat of vaporization (Hv) for water is 2260 J/g.
The formula to calculate the heat (q) required is q = mcΔT + mHv, where m is the mass (200g), c is the specific heat capacity, and ΔT is the change in temperature.
q3 = (200g) * (4.18 J/g°C) * (100°C - 0°C) + (200g) * (2260 J/g)
q3 = 83,600 J + 452,000 J
q3 = 535,600 J
Now, to find the total heat required, add the heat values of each stage together:
Total heat = q1 + q2 + q3
Total heat = 836 J + 66,800 J + 535,600 J
Total heat = 603,236 J
Therefore, the amount of heat required to convert 200g of ice cubes from 0°C to gas at 100°C is 603,236 Joules.