91Ó°ÊÓ

Potential energy is the energy stored in an object due to its position relative to a source of gravity. In this exercise, the rock has potential energy because it is at a height above the surface of the lake. The formula used to calculate potential energy is given by:
\( PE = m \cdot g \cdot h \)
where:

• \( m \) is the mass of the rock in kilograms (kg)
• \( g \) is the acceleration due to gravity, approximately \( 9.81 \, \text{m/s}^2 \)
• \( h \) is the height in meters (m)

As the rock falls, its potential energy is converted into kinetic energy. Upon hitting the water, the potential energy the rock had at the height will be transformed and can contribute to changes in thermal and entropy states of the surrounding environment.

Temperature change refers to the difference in temperature that an object experiences over time or between two separate states. In this problem, the rock originally at different temperatures before and after dropping undergoes different interactions with the lake's water.
For case (a), there is no temperature change when the rock (initially at \(20^{\circ} \text{C}\)) is placed in water also at \(20^{\circ} \text{C}\). Therefore, no net heat exchange directly affects temperature.
In case (b), the temperature initially at \(100^{\circ} \text{C}\) drops due to heat exchange with the lake water (which is at \(20^{\circ} \text{C}\)). The difference \( \Delta T \) is \(80^{\circ} \text{C}\). It plays a crucial role in determining the heat exchange, which subsequently affects entropy.

Specific heat is a property of a material that measures how much heat energy is needed to change the temperature of a unit mass by one degree. It is essential in determining how a material reacts to temperature changes during heat transfer processes. The formula to calculate the heat energy (\(Q\)) is:
\( Q = m \cdot c \cdot \Delta T \)
where:

• \( Q \) is the heat energy in joules (J)
• \( c \) is the specific heat capacity of the material (for the rock, \(860 \, \text{J/kg} \cdot \text{K}\))
• \( \Delta T \) is the temperature change in degrees Celsius or Kelvin

Using the specific heat, one can determine how the rock's higher initial temperature affects energy transfer, illustrating the concepts of energy conservation and transition between systems.

Heat exchange occurs when heat energy transfers between objects or systems. This commonly arises due to difference in temperature, as energy naturally flows from hotter to cooler areas until equilibrium is reached.
In the context of the exercise, once the rock hits the lake, it loses heat to the surrounding water in case (b) because its initial temperature exceeds that of the water. Using the previous sections, we calculate the heat exchange amount:
\( Q = 5 \times 860 \times 80 \)
This equation helps in deriving the alteration in entropy, factoring in both potential energy loss and heat dispersion, affecting the universe's overall entropy. Understanding heat exchange supports concepts of thermodynamics, especially regarding energy dispersion and equilibrium tendencies.