How much total heat is required to heat 3316 g of ice at -16.12 oC to all steam at a temperature of 128.08 oC?
how do you carry out the five step process?
To determine the total heat required to heat a substance through a temperature range and phase change, you can follow a five-step process:
Step 1: Calculate the heat required to heat the ice from -16.12°C to 0°C.
Step 2: Calculate the heat required to melt the ice at 0°C to water at 0°C.
Step 3: Calculate the heat required to heat the water from 0°C to 100°C.
Step 4: Calculate the heat required to convert the water at 100°C to steam at 100°C.
Step 5: Calculate the heat required to heat the steam from 100°C to 128.08°C.
Let's carry out each step.
Step 1: Calculate the heat required to heat the ice from -16.12°C to 0°C.
The specific heat capacity of ice is typically 2.09 J/g°C.
q1 = mass × specific heat capacity × change in temperature
q1 = 3316 g × 2.09 J/g°C × (0°C - (-16.12°C))
q1 = 3316 g × 2.09 J/g°C × 16.12°C
q1 = 109,534.9128 J
Step 2: Calculate the heat required to melt the ice at 0°C to water at 0°C.
The specific heat of fusion (heat of melting) for ice is usually 334 J/g.
q2 = mass × specific heat of fusion
q2 = 3316 g × 334 J/g
q2 = 1,105,944 J
Step 3: Calculate the heat required to heat the water from 0°C to 100°C.
The specific heat capacity of water is generally around 4.18 J/g°C.
q3 = mass × specific heat capacity × change in temperature
q3 = 3316 g × 4.18 J/g°C × (100°C - 0°C)
q3 = 1,382,904.8 J
Step 4: Calculate the heat required to convert the water at 100°C to steam at 100°C.
The molar heat of vaporization for water is approximately 40.7 kJ/mol, which is equivalent to 40.7 J/g.
q4 = mass × molar heat of vaporization
q4 = 3316 g × 40.7 J/g
q4 = 134,706.8 J
Step 5: Calculate the heat required to heat the steam from 100°C to 128.08°C.
The specific heat capacity of steam is usually 2.03 J/g°C.
q5 = mass × specific heat capacity × change in temperature
q5 = 3316 g × 2.03 J/g°C × (128.08°C - 100°C)
q5 = 229,510.28 J
Finally, calculate the total heat required:
Total heat = q1 + q2 + q3 + q4 + q5
Total heat = 109,534.9128 J + 1,105,944 J + 1,382,904.8 J + 134,706.8 J + 229,510.28 J
Total heat ≈ 3,962,600 J
Therefore, approximately 3,962,600 Joules of heat is required to heat 3316 g of ice at -16.12°C to steam at a temperature of 128.08°C.
To carry out the five-step process to solve this question, follow these steps:
Step 1: Determine the phases involved and the temperature changes each phase undergoes.
- In this question, we have ice at -16.12 oC, which needs to be heated to its melting point, then melted, then heated to the boiling point, and finally, turned into steam at 128.08 oC.
Step 2: Calculate the heat required to change the temperature of each phase.
- To calculate the heat required to change the temperature of a substance, you can use the formula: q = mcΔT.
- q represents the heat required, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
- For ice, the specific heat capacity is 2.09 J/g·°C, and the change in temperature is the final temperature (0 oC) minus the initial temperature (-16.12 oC).
- Calculate the heat required to heat ice from -16.12 oC to its melting point (0 oC) using the mass of the ice.
Step 3: Calculate the heat required for phase changes.
- To melt ice, you need to calculate the heat required using the formula: q = mΔHf.
- ΔHf is the heat of fusion, which represents the energy needed to convert a substance from solid to liquid at its melting point.
- For ice, the heat of fusion is 334 J/g.
- Calculate the heat required to melt the ice using the mass of the ice.
Step 4: Calculate the heat required to change the temperature of water to the boiling point.
- Use the same formula as in Step 2 to calculate the heat required to change the temperature of water from 0 oC to the boiling point at 100 oC.
- The specific heat capacity of water is 4.18 J/g·°C.
- Calculate the heat required using the mass of the liquid water.
Step 5: Calculate the heat required for the vaporization of water.
- To turn water into steam, you need to calculate the heat required using the formula: q = mΔHv.
- ΔHv is the heat of vaporization, which represents the energy needed to convert a substance from liquid to gas at its boiling point.
- For water, the heat of vaporization is 2260 J/g.
- Calculate the heat required to convert water into steam using the mass of the water.
Finally, add up all the calculated heats from the previous steps to obtain the total heat required to heat the given amount of ice to steam at the stated temperatures.
Heat needed to raise the temperature of ice from -16.12c to 0c=mcT
=3.316*2100*16.12
=112253.23 joules
Heat to melt the ice=mL
=3.316*336000
=1114176 joules
Heat needed to raise the temperature of the water from 0c to 100c=mcT
=3.316*4200*100
=1392720 joules
Heat needed to vaporise 3.316kg of water=mL
=3.316*2260000
=7494160 joules
Heat needed to raise the temperature of steam from 100c to 128.8c=mcT
=3.316*2100*28.8
=200551.68 joules
Total heat required= 112253.23+1114176+1392720+7494160+200551.68
=10313860 joules