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The concept of latent heat of vaporization is crucial when studying phase changes between steam and water. When a substance, like water, changes its phase from liquid to gas or vice versa, energy is either absorbed or released in the process. This energy is the latent heat of vaporization. For water, this is approximately 2260 kJ/kg.
This means when 1 kg of water condenses from steam to liquid, it releases 2260 kJ of energy. In the context of the exercise, the condensation of 0.0400 kg of steam releases energy into the water. The formula used to calculate this is:

• \[ Q_{condensation} = m_{steam} \cdot L_v \]

Where \( Q_{condensation} \) is the heat released, \( m_{steam} \) is the mass of steam, and \( L_v \) is the latent heat of vaporization. Understanding this principle helps in determining the heat transfer during the phase change, as seen in the original solution.

Thermal Equilibrium is a state where two or more substances reach the same temperature, and no heat flows between them. In the given exercise, steam and water must transfer heat between each other until they reach a common final temperature.
To achieve this, the total heat lost by the steam as it condenses and cools should equal the total heat gained by the water. The heat balance equation represents this concept:

• \[ Q_{condensation} + Q_{cooling} = Q_{water} \]

Here, \( Q_{cooling} \) is the heat lost as the condensed steam cools to the final temperature, and \( Q_{water} \) is the heat gained by the water initially at 50°C. By setting up and solving this equation, the final equilibrium temperature \( T_f \) is determined, illustrating how thermal equilibrium is achieved.

Specific heat capacity is the amount of heat required to change a unit mass of a substance by one degree Celsius. For water, this value is approximately 4.18 kJ/kg°C. It's an important parameter when dealing with temperature changes in substances without a change of state.
In the exercise, when the steam condenses and releases heat, the specific heat capacity of water is used to calculate additional heat required to change the temperature of both the condensed steam and the initial water to the final equilibrium temperature.
The formulas used are:

• For cooling condensed steam:\[ Q_{cooling} = m_{condensed} \cdot c_w \cdot (100^{\circ}C - T_f) \]
• For initial water gaining heat:\[ Q_{water} = m_{water} \cdot c_w \cdot (T_f - 50^{\circ}C) \]

Here \( c_w \) is the specific heat capacity of water. Understanding specific heat capacity helps us determine how much energy is transferred during the heat exchange process to reach thermal equilibrium.