How many joules of energy are needed to change 114 g of water at 16.5°C to steam at 100°C?
Look at your ice to steam problem above. This is the same concept. After you have one of these worked you should be able to follow the template and work the others.
In these problems there are two formulas.
1. When changing T WITHIN A PHASE (i.e., one T in ice to another T in ice or one T in liquid to another T in liquid), the formula is q = mass x specific heat in that phase x (Tfinal-Tinitial)
2. When changing the PHASE (at the melting point from solid to liquid or at the boiling point from liquid to vapor) it is
a. mass solid x heat fusion or
b. mass liquid x heat vaporization.
Those three formulas will take you from any point on the scale to any other point on the scale.
To find the amount of energy required to change the water to steam, we need to consider two separate steps:
1. Heating the water from its initial temperature of 16.5°C to its boiling point of 100°C (phase change from liquid to gas).
2. Vaporizing the water at its boiling point (phase change from liquid to gas).
Let's calculate the amount of energy required for each step:
Step 1: Heating the water from 16.5°C to 100°C
The specific heat capacity of water is approximately 4.184 J/g°C. Therefore, to calculate the energy needed to raise the temperature of the water, we can use the formula:
E = m * c * ΔT
Where:
E: Energy (in joules)
m: Mass of water (in grams)
c: Specific heat capacity of water (in J/g°C)
ΔT: Temperature change (in °C)
Plugging in the values:
E1 = 114 g * 4.184 J/g°C * (100°C - 16.5°C)
Step 2: Vaporizing the water at its boiling point
The heat of vaporization for water is approximately 2260 J/g. Therefore, to calculate the energy needed to vaporize the water, we can use the formula:
E = m * Hv
Where:
E: Energy (in joules)
m: Mass of water (in grams)
Hv: Heat of vaporization (in J/g)
Plugging in the values:
E2 = 114 g * 2260 J/g
Finally, to find the total energy required, we add E1 and E2 together:
Total energy = E1 + E2
By plugging in the calculations above, we can determine the total energy needed to change the water to steam.