How much heat is necessary to change a 52.0 g sample of water at 33.0 C into steam at 110.0 C?
To find the amount of heat necessary to change the water at 33.0°C into steam at 110.0°C, we need to consider the different steps involved in this process:
1. Heating the water from 33.0°C to its boiling point, which is 100.0°C.
2. Converting the water at its boiling point into steam at the same temperature.
3. Heating the steam from 100.0°C to 110.0°C.
To calculate the heat required for each step, we can use the following formulas:
1. Heat required to raise the temperature of a substance:
Q₁ = m * c * ΔT₁
where Q₁ is the heat required, m is the mass of the substance, c is the specific heat capacity, and ΔT₁ is the change in temperature.
2. Heat required for a phase change (in this case, converting water to steam):
Q₂ = m * ΔHv
where Q₂ is the heat required, m is the mass of the substance, and ΔHv is the enthalpy of vaporization.
3. Heat required to raise the temperature of a substance:
Q₃ = m * c * ΔT₂
where Q₃ is the heat required, m is the mass of the substance, c is the specific heat capacity, and ΔT₂ is the change in temperature.
Let's calculate the heat required for each step:
Step 1:
Q₁ = m * c * ΔT₁
= 52.0 g * 4.18 J/g°C * (100.0°C - 33.0°C)
Step 2:
Q₂ = m * ΔHv
= 52.0 g * 2.26 J/g
(Note: The enthalpy of vaporization for water is 2.26 J/g)
Step 3:
Q₃ = m * c * ΔT₂
= 52.0 g * 2.03 J/g°C * (110.0°C - 100.0°C)
To find the total amount of heat required, we add up the heat required for each step:
Total heat = Q₁ + Q₂ + Q₃
Performing the calculations will yield the answer in joules (J).