Calculating Energy Change When Water Converts To Steam

The fascinating world of chemistry often involves observing and quantifying energy changes during various processes. One such process, and a very fundamental one at that, is the phase transition of water. When water transitions from its liquid state to its gaseous state (steam) at a constant temperature and pressure, a significant amount of energy is absorbed. This absorbed energy, primarily utilized to overcome the intermolecular forces holding the water molecules together in the liquid state, is a crucial concept to grasp in thermodynamics. In this article, we will delve into the specific scenario where one mole of water at 100°C and 1 atm pressure is converted into steam at the same temperature and pressure, with a heat absorption of 40670 Joules. We will carefully calculate and discuss the various energy changes involved in this process, including the change in internal energy (ΔU) and the change in enthalpy (ΔH), providing a comprehensive understanding of the thermodynamics at play.

The question presented gives us a classic example of a phase transition occurring at constant temperature and pressure. When one mole of water at 100°C and 1 atm pressure transforms into steam at the same conditions, it absorbs 40670 Joules of heat. This heat absorption is known as the enthalpy change of vaporization (ΔHvap). Let's break down the calculation and the underlying principles to fully comprehend the energy transformation happening at a molecular level. Understanding these calculations is crucial for various applications, from designing efficient steam engines to predicting weather patterns. The accurate determination of energy changes during phase transitions is also vital in industrial processes such as distillation and evaporation, where precise control of temperature and pressure is essential for optimal efficiency and product yield.

Enthalpy Change (ΔH)

In chemical thermodynamics, enthalpy (H) is a crucial property of a thermodynamic system, defined as the sum of the system's internal energy (U) and the product of its pressure (P) and volume (V): H = U + PV. Enthalpy is often used to measure the heat exchanged in a chemical reaction or physical transformation that occurs at constant pressure, which is a common condition in many laboratory and industrial settings. The enthalpy change (ΔH) represents the amount of heat absorbed or released during a process at constant pressure. A positive ΔH indicates an endothermic process (heat absorbed), while a negative ΔH indicates an exothermic process (heat released). In the scenario presented, the heat absorbed during the conversion of one mole of water to steam at 100°C and 1 atm is given as 40670 Joules. This value directly represents the enthalpy change (ΔH) for this process.

• ΔH = 40670 J

This positive value confirms that the vaporization of water is an endothermic process, requiring energy input to overcome the intermolecular forces holding the water molecules together in the liquid phase. The magnitude of ΔH provides insight into the strength of these intermolecular forces and the amount of energy needed to transition the substance from a liquid to a gaseous state. Understanding enthalpy changes is essential in various fields, including chemical engineering, materials science, and environmental science, where energy management and process optimization are critical.

Internal Energy Change (ΔU)

Internal energy (U) is a fundamental concept in thermodynamics, representing the total energy contained within a thermodynamic system. It encompasses various forms of energy, including the kinetic energy of the molecules (due to their motion) and the potential energy associated with intermolecular forces and chemical bonds. The change in internal energy (ΔU) reflects the net change in these energy components during a process. To determine the internal energy change (ΔU) for the vaporization of water, we can use the following thermodynamic relationship:

• ΔH = ΔU + PΔV

Where:

• ΔH is the enthalpy change
• ΔU is the internal energy change
• P is the pressure (constant at 1 atm)
• ΔV is the change in volume

To calculate ΔU, we first need to determine the change in volume (ΔV). Since we are dealing with the phase transition from liquid water to steam, the volume change will be significant due to the much larger molar volume of steam compared to liquid water. We can use the ideal gas law to approximate the volume of steam:

• PV = nRT

Where:

• P is the pressure (1 atm)
• V is the volume
• n is the number of moles (1 mole)
• R is the ideal gas constant (8.314 J/mol·K)
• T is the temperature (100°C = 373.15 K)

First, we calculate the volume of steam (V_steam):

• V_steam = (nRT) / P
• V_steam = (1 mol * 8.314 J/mol·K * 373.15 K) / 1 atm

We need to convert the pressure from atm to Pascals (Pa) since the gas constant R is in J/mol·K, and 1 atm = 101325 Pa.

• V_steam = (1 mol * 8.314 J/mol·K * 373.15 K) / 101325 Pa
• V_steam ≈ 0.0306 m³

Next, we need to estimate the volume of liquid water (V_water). The molar volume of liquid water at 100°C is approximately 18 × 10⁻⁶ m³/mol.

Now, we can calculate the change in volume (ΔV):

• ΔV = V_steam - V_water
• ΔV ≈ 0.0306 m³ - 18 × 10⁻⁶ m³
• ΔV ≈ 0.0306 m³

Now we can calculate the internal energy change (ΔU) using the formula:

• ΔU = ΔH - PΔV
• ΔU = 40670 J - (101325 Pa * 0.0306 m³)
• ΔU = 40670 J - 31005.45 J
• ΔU ≈ 9664.55 J

Therefore, the internal energy change (ΔU) for the conversion of one mole of water to steam at 100°C and 1 atm is approximately 9664.55 Joules. This value represents the energy that goes into increasing the kinetic energy of the water molecules and overcoming the intermolecular forces in the liquid phase.

The calculations above highlight the significant energy changes that occur during a phase transition. The enthalpy change (ΔH) of 40670 J represents the total heat absorbed during the vaporization process, while the internal energy change (ΔU) of approximately 9664.55 J reflects the energy utilized to increase the kinetic energy of the water molecules and overcome intermolecular attractions. The difference between ΔH and ΔU is the work done by the system to expand against the constant external pressure as water transforms into steam.

Significance of Enthalpy Change (ΔH)

The enthalpy change (ΔH) for the vaporization of water is substantial due to the relatively strong hydrogen bonds present in liquid water. These hydrogen bonds create a network of intermolecular attractions that require significant energy input to overcome. The large ΔH value explains why it takes a considerable amount of energy to boil water, which has significant implications for various natural and industrial processes. For example, the high heat of vaporization of water plays a crucial role in regulating Earth's climate by absorbing a large amount of heat during evaporation, which helps to cool the environment. This phenomenon is particularly important in tropical regions, where evaporation is high due to the abundance of water and solar energy.

In industrial applications, the large ΔH of water vaporization is utilized in processes such as steam power generation, where water is heated and converted into steam to drive turbines and generate electricity. The efficiency of these power plants depends significantly on the enthalpy of vaporization of water. Furthermore, the high ΔH value is exploited in cooling systems, where water is evaporated to absorb heat from the surroundings, providing effective cooling. Understanding and accurately quantifying the enthalpy change of vaporization is therefore essential in optimizing these industrial processes and designing efficient energy systems.

Significance of Internal Energy Change (ΔU)

The internal energy change (ΔU), while smaller than the enthalpy change, provides insights into the energy distribution within the system. The positive ΔU value indicates that a portion of the heat absorbed goes into increasing the internal energy of the system, primarily by increasing the kinetic energy of the water molecules as they transition from liquid to gas. This increase in kinetic energy is directly related to the higher temperature and increased molecular motion in the gaseous state.

The difference between ΔH and ΔU (approximately 31005.45 J in this case) represents the work done by the system to expand against the constant external pressure. This work is a direct consequence of the significant increase in volume when water vaporizes. The work done against the surroundings is a crucial component in thermodynamic analyses, particularly in understanding the efficiency of energy conversion processes. In the context of water vaporization, this work represents the energy expended to create space for the steam molecules, overcoming the atmospheric pressure.

Implications for Various Fields

The principles and calculations discussed here have broad implications across various scientific and engineering disciplines:

• Meteorology: Understanding the heat of vaporization of water is crucial for modeling weather patterns and climate change. The evaporation and condensation of water in the atmosphere play a significant role in energy transfer and temperature regulation.
• Chemical Engineering: In chemical processes involving phase transitions, accurate knowledge of enthalpy and internal energy changes is essential for designing efficient and cost-effective processes.
• Mechanical Engineering: Steam power generation, refrigeration, and air conditioning systems rely on the principles of thermodynamics, including the enthalpy of vaporization of working fluids.
• Environmental Science: The evaporation of water from natural bodies plays a vital role in the hydrological cycle and the transport of pollutants. Understanding the energy requirements for evaporation helps in modeling these processes.

In conclusion, the conversion of one mole of water at 100°C and 1 atm pressure to steam at the same conditions involves a significant absorption of heat (40670 J), primarily due to the energy required to overcome the intermolecular forces in liquid water. This heat absorption is represented by the enthalpy change (ΔH). The internal energy change (ΔU) is approximately 9664.55 J, indicating the energy utilized to increase the kinetic energy of the water molecules during the phase transition. The difference between ΔH and ΔU accounts for the work done by the system to expand against the constant external pressure.

The understanding of these energy changes is fundamental in various fields, including chemistry, physics, engineering, and environmental science. Accurate calculations and interpretations of enthalpy and internal energy changes are essential for designing efficient industrial processes, modeling weather patterns, and comprehending the thermodynamics of phase transitions. The principles discussed in this article provide a solid foundation for further exploration into the fascinating world of thermodynamics and its applications.