Assume that the pressure is one atmosphere and determine the heat in joules required to produce 2.99 kg of water vapor at 100.0 °C, starting with (a)2.99 kg of water at 100.0 °C and (b)2.99 kg of liquid water at 0.0 °C.
To determine the heat required to produce water vapor, we need to consider two scenarios:
(a) Starting with 2.99 kg of water at 100.0 °C:
In this case, we need to calculate the heat required to convert all of the water to steam at the boiling point. Here's how you can calculate it:
1. Determine the heat required to raise the temperature of the water to its boiling point:
- The specific heat capacity of liquid water is 4.18 J/g°C.
- The change in temperature is the difference between the boiling point (100.0 °C) and the initial temperature (100.0 °C).
- Calculate the heat using the formula: Q = m * C * ΔT,
where Q is the heat, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.
2. Determine the heat required to convert the water to steam:
- The heat required to convert 1 gram of water to steam at its boiling point is called the heat of vaporization. For water, it is approximately 40.7 kJ/g.
- Calculate the heat using the formula: Q = m * H,
where Q is the heat, m is the mass of water, and H is the heat of vaporization.
3. Add the two calculated heats to get the total heat required to produce water vapor.
(b) Starting with 2.99 kg of liquid water at 0.0 °C:
In this case, we need to calculate the heat required to raise the temperature of the water to its boiling point and then convert it to steam. Here's how you can calculate it:
1. Determine the heat required to raise the temperature of the water to its boiling point:
- The specific heat capacity of liquid water is 4.18 J/g°C.
- The change in temperature is the difference between the boiling point (100.0 °C) and the initial temperature (0.0 °C).
- Calculate the heat using the formula: Q = m * C * ΔT,
where Q is the heat, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.
2. Determine the heat required to convert the liquid water to steam:
- The heat required to convert 1 gram of water to steam at its boiling point is called the heat of vaporization. For water, it is approximately 40.7 kJ/g.
- Calculate the heat using the formula: Q = m * H,
where Q is the heat, m is the mass of water, and H is the heat of vaporization.
3. Add the two calculated heats to get the total heat required to produce water vapor.
Assuming you have the values for mass and specific heat capacity, you can plug them into the formulas and calculate the heat in joules required to produce water vapor in both scenarios.