The specific heat capacity of ice is about 0.5 cal/g °C. Calculate the number of calories it would take to change a 4 gram ice cube at absolute zero (-273°C) to 4 gram of boiling water.
add the heats:
heat to warm ice to zero
heat to melt ice at zero
heat to warm melted ice from zero to 100.
That puts it to 100. any heat after that starts boiling.
To calculate the number of calories it would take to change a 4 gram ice cube at absolute zero (-273°C) to 4 grams of boiling water, we need to consider the following steps:
Step 1: Heating the ice from absolute zero to its melting point:
The specific heat capacity of ice is given as 0.5 cal/g °C.
Since the ice is initially at -273°C and needs to reach its melting point at 0°C, we need to calculate the heat required for this step.
Heat = mass x specific heat capacity x change in temperature
Mass of ice = 4 grams
Specific heat capacity of ice = 0.5 cal/g °C
Change in temperature = (0°C - (-273°C)) = 273°C
Heat = 4 grams * 0.5 cal/g °C * 273 °C
Heat = 546 cal
Step 2: Melting the ice:
When ice melts, heat energy is absorbed without a change in temperature.
The heat required to melt ice can be calculated using the formula:
Heat = mass x heat of fusion
Mass of ice = 4 grams
Heat of fusion of ice = 80 cal/g
Heat = 4 grams * 80 cal/g
Heat = 320 cal
Step 3: Heating the water from its melting point to its boiling point:
The specific heat capacity of water is approximately 1 cal/g °C.
Since the water is initially at 0°C and needs to reach its boiling point at 100°C, we need to calculate the heat required for this step.
Heat = mass x specific heat capacity x change in temperature
The mass of water is still 4 grams, and the specific heat capacity of water is 1 cal/g °C.
Change in temperature = 100°C - 0°C = 100°C
Heat = 4 grams * 1 cal/g °C * 100°C
Heat = 400 cal
Step 4: Boiling the water:
When water boils, heat energy is absorbed without a change in temperature.
The heat required to boil water can be calculated using the formula:
Heat = mass x heat of vaporization
The mass of water is still 4 grams, and the heat of vaporization of water is approximately 540 cal/g.
Heat = 4 grams * 540 cal/g
Heat = 2160 cal
Now, to find the total heat required, we sum up the heat for each step:
Total heat = Heat from step 1 + Heat from step 2 + Heat from step 3 + Heat from step 4
Total heat = 546 cal + 320 cal + 400 cal + 2160 cal
Total heat = 3426 cal
Therefore, it would take approximately 3426 calories to change a 4 gram ice cube at absolute zero (-273°C) to 4 grams of boiling water.
To calculate the number of calories it would take to change a 4 gram ice cube at absolute zero (-273°C) to 4 grams of boiling water, we can use the formula:
Q = m * c * ΔT
Where Q is the heat energy required, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
First, let's calculate the heat energy required to warm up the ice cube from -273°C to 0°C:
Q1 = m * c * ΔT1
= 4g * 0.5 cal/g °C * (0°C - (-273°C))
= 4g * 0.5 cal/g °C * 273°C
= 546 cal
Next, we need to calculate the heat energy required to melt the ice at 0°C:
Q2 = m * L
= 4g * 79.7 cal/g
= 319 cal
Where L is the heat of fusion (the energy required to change a substance from solid to liquid at its melting point). For ice, the heat of fusion is 79.7 cal/g.
Now, let's calculate the heat energy required to warm up the water from 0°C to its boiling point:
Q3 = m * c * ΔT2
= 4g * 1 cal/g °C * (100°C - 0°C)
= 4g * 1 cal/g °C * 100°C
= 400 cal
Finally, we need to calculate the heat energy required to vaporize the water at its boiling point:
Q4 = m * L
= 4g * 540 cal/g
= 2160 cal
Where L is the heat of vaporization (the energy required to change a substance from liquid to gas at its boiling point). For water, the heat of vaporization is 540 cal/g.
Now, we can calculate the total heat energy required:
Total Q = Q1 + Q2 + Q3 + Q4
= 546 cal + 319 cal + 400 cal + 2160 cal
= 3425 calories
Therefore, it would take approximately 3425 calories of heat energy to change a 4 gram ice cube at absolute zero (-273°C) to 4 grams of boiling water.