91Ó°ÊÓ

In physics, kinetic energy is the energy an object possesses due to its motion. The faster an object moves, the more kinetic energy it has. The formula to calculate kinetic energy is given by \( KE = \frac{1}{2} mv^2 \), where \( m \) is the mass and \( v \) is the velocity of the object.
In the given exercise, the initial and final velocities of the cylindrical mass are provided. We can calculate the initial kinetic energy using the formula:
\[ KE_{initial} = \frac{1}{2} \times 5 \times 30^2 \]
which equals 2.25 kJ. Similarly, the final kinetic energy is calculated as:
\[ KE_{final} = \frac{1}{2} \times 5 \times 15^2 \]
which equals 0.5625 kJ. The change in kinetic energy is then:
\[ \Delta KE = KE_{final} - KE_{initial} = 0.5625 - 2.25 = -1.6875 kJ \]

Internal energy is the total energy contained within a system, related to both the microscopic kinetic and potential energies of its particles. It is an intrinsic property and is different from kinetic and potential energy which are macroscopic forms of energy.
In this problem, the specific internal energy (energy per kilogram) changes from 1.2 kJ/kg to 1.9 kJ/kg. To find the total change in internal energy, we use the formula:
\[ \Delta U = m \times ( u_{final} - u_{initial} ) \]
Given the mass is 5 kg, we plug in the values:
\[ \Delta U = 5 \times (1.9 - 1.2) = 5 \times 0.7 = 3.5 kJ \]
This indicates an increase in the internal energy of the system by 3.5 kJ.

Heat transfer is the exchange of thermal energy between physical systems. The heat transfer can be through conduction, convection, or radiation. In this problem, the mass receives heat via its bottom surface and loses it through its top surface.
The amount of heat added to the system is 2 kJ, while the heat lost is 1 kJ. The net heat transfer (Q) to the system can be calculated as:
\[ Q = 2 \text{kJ} - 1 \text{kJ} = 1 \text{kJ} \]
This net heat transfer is crucial in applying the First Law of Thermodynamics to find the work done or energy change in the system.

The First Law of Thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed in an isolated system. It can only be transformed from one form to another. The mathematical representation of this law is:
\[ Q - W = \Delta U + \Delta KE \]
where \( Q \) is heat added to the system, \( W \) is work done by the system, \( \Delta U \) is the change in internal energy, and \( \Delta KE \) is the change in kinetic energy.
Using the given values:
\[ Q = 1 \text{kJ}, \Delta U = 3.5 \text{kJ}, \Delta KE = -1.6875 \text{kJ} \]
we rearrange the formula to solve for work (W):
\[ W = Q - \Delta U - \Delta KE = 1 - 3.5 - (-1.6875) = 1 - 3.5 + 1.6875 = -0.8125 \text{kJ} \]
Hence, the work done by the system in this process is -0.8125 kJ.