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When a substance transforms from one state of matter to another, it's known as a phase change. In our context, water is changing from a liquid to a gaseous state. This is called vaporization or boiling. This transition occurs at a specific temperature and pressure, in this case, at \(100^{\circ} \mathrm{C}\) and \(1.0\) atm. During a phase change, energy is added or removed from the system without altering its temperature, ensuring the substance undergoes a transformation.

• Melting and Freezing: Phase change between solid and liquid.
• Vaporization and Condensation: Phase change between liquid and gas.

Understanding phase changes helps us address how energy inputs impact the state of a material. For water, this is crucial since it allows us to calculate the work done and changes in energy when it turns into steam.

Latent heat is the energy absorbed or released by a substance during a phase change at a constant temperature and pressure. Unlike sensible heat, which changes the temperature of a substance, latent heat does not alter the temperature but changes its state instead.

• Latent Heat of Fusion: The heat required to convert a solid into a liquid without temperature change.
• Latent Heat of Vaporization: The heat required to convert a liquid into a gas without temperature change.

In the given problem, the latent heat of vaporization \(L_v\) is \(540 \mathrm{cal} / \mathrm{g}\). This implies that each gram of water absorbs 540 calories to become steam at \(100^{\circ} \mathrm{C}\), facilitating the phase change without a change in temperature.

Internal energy is the total energy contained within a system due to its particles' motion and position. It includes kinetic and potential energies at a microscopic scale. In the context of phase changes, internal energy is influenced by the heat absorbed and the work done by the system.
To find the change in internal energy during phase changes, we use the formula:\[\Delta U = Q - W\]where \(\Delta U\) is the change in internal energy, \(Q\) is the heat absorbed, and \(W\) is the work done by the system. For the system in question, converting 1 g of water to steam results in an internal energy increase of approximately 2096.31 Joules. This reflects the energy required for the phase transition plus the work done against the atmospheric pressure.

Work done is a concept from physics that describes the energy transferred by a force over a distance. In thermodynamics, it represents the energy required for a system to expand or contract.
In the scenario of boiling water turning into steam, work is done by the system when the volume of water vapor increases. To calculate work done, we use the formula:\[ W = P \Delta V \]where \(P\) is the external pressure (1 atm) and \(\Delta V\) is the change in volume (1670 cm³ - 1 cm³). The work needed for this phase change, calculated in the solution, is approximately 169.05 Joules. This \(W\) signifies the energy transferred to push against the atmospheric pressure, allowing the water to expand into steam.