Boiling Water at High Pressure. When water is boiled at a pressure of 2.00 atm, the heat of vaporization is 2.20 * 10^6 J/kg and the boiling point is 120°C. At this pressure, 1.00 kg of water has a volume of 1.00 * 10^-3 m^3 , and 1.00 kg of steam has a volume of 0.824 m^3. (a) Compute the work done when 1.00 kg of steam is formed at this temperature.

Verified step by step guidance

1. Identify the initial and final volumes of the water and steam. The initial volume when water is in liquid form is 1.00 * 10^-3 m^3, and the final volume when it turns into steam is 0.824 m^3.
2. Calculate the change in volume, \( \Delta V \), which is the final volume minus the initial volume. Use the formula: \( \Delta V = V_{final} - V_{initial} \).
3. Use the formula for work done during a constant pressure process, which is given by \( W = P \Delta V \), where \( P \) is the pressure and \( \Delta V \) is the change in volume.
4. Substitute the values into the formula: \( P = 2.00 \, \text{atm} \) (convert this to Pascals if necessary using the conversion 1 atm = 101325 Pa) and the \( \Delta V \) calculated in step 2.
5. Calculate the work done, which will be in Joules, using the substituted values.

Key Concepts

Heat of Vaporization

The heat of vaporization is the amount of energy required to convert a unit mass of a substance from liquid to gas at constant temperature and pressure. For water, this value is significant because it determines how much energy must be supplied to boil water. In this case, the heat of vaporization is given as 2.20 * 10^6 J/kg, indicating the energy needed to convert 1 kg of water into steam at 2.00 atm.

Work Done in Phase Change

When a substance undergoes a phase change, such as from liquid to gas, work can be done on or by the system due to changes in volume. The work done during the formation of steam can be calculated using the formula W = PΔV, where P is the pressure and ΔV is the change in volume. In this scenario, the volume of steam is significantly larger than that of water, leading to positive work done by the system as it expands.

Ideal Gas Law and Phase Behavior

The Ideal Gas Law (PV = nRT) describes the behavior of gases under various conditions of pressure, volume, and temperature. Although steam behaves like an ideal gas under certain conditions, it is important to consider the phase behavior of water at high pressures. The boiling point of water increases with pressure, as indicated by the boiling point of 120°C at 2.00 atm, which affects the calculations of work and energy during the phase transition.