How many joules of energy are needed to change 275 g of water from 15°C to steam at 100.°C?
q1 = heat needed to raise T from 15 C to 100 C.
q1 = mass H2O x specific heat H2O x (Tfinal-T(intial)
q2 = heat need to change liquid H2O to vapor.
q2 = mass H2O x heat vaporization
Total Q = q1 +q2
To find the amount of energy required to change the temperature of water from 15°C to steam at 100°C, we need to consider two separate processes: heating the water from 15°C to its boiling point (100°C) and vaporizing the water.
First, let's calculate the energy required to heat the water from 15°C to its boiling point. This can be done using the specific heat capacity formula:
Q = m * c * ΔT
Where:
Q is the energy transferred in joules.
m is the mass of the water in grams.
c is the specific heat capacity of water (4.18 J/g°C).
ΔT is the change in temperature (final temperature - initial temperature).
In this case, the mass (m) is 275 g, the specific heat capacity (c) is 4.18 J/g°C, and the change in temperature (ΔT) is 100°C - 15°C = 85°C.
Q = 275 g * 4.18 J/g°C * 85°C
Q = 99877.5 J (rounded to the nearest joule)
The energy required to heat the water to its boiling point is approximately 99877.5 joules.
Next, let's calculate the energy required to vaporize the water at its boiling point. This can be done using the formula:
Q = m * Lv
Where:
Q is the energy transferred in joules.
m is the mass of the water in grams.
Lv is the heat of vaporization of water (2260 J/g).
In this case, the mass (m) is 275 g, and the heat of vaporization (Lv) is 2260 J/g.
Q = 275 g * 2260 J/g
Q = 621,500 J (rounded to the nearest joule)
The energy required to vaporize the water is approximately 621,500 joules.
Finally, to find the total energy required, we add the energy for heating the water and the energy for vaporization:
Total energy = heating energy + vaporization energy
Total energy = 99877.5 J + 621,500 J
Total energy = 721,377.5 J (rounded to the nearest joule)
Therefore, approximately 721,377.5 joules of energy are needed to change 275 g of water from 15°C to steam at 100°C.