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Kinetic energy is a type of energy that a moving object possesses because of its motion. It is given by the formula \( K.E. = \frac{1}{2} m v^2 \), where \( m \) is the mass of the object and \( v \) is its velocity. In our subway train example, the train possesses kinetic energy because it is moving at an initial velocity of 15.5 meters per second before it slows down to a stop. To calculate the initial kinetic energy of the train:- Plug in the mass of the train, \( m = 25000 \, \text{kg} \), and the velocity, \( v = 15.5 \, \text{m/s} \), into the equation.- The initial kinetic energy is found to be: \[ K.E. = \frac{1}{2} \times 25000 \times (15.5)^2 \]Understanding how kinetic energy works helps us predict how much work is needed to bring the train to a halt. In this case, all the work done to stop the train is converted into heat energy, which is why knowing how to calculate kinetic energy is essential for our problem.

Specific heat capacity is a physical property that shows how much energy is needed to change the temperature of a unit mass of a substance by one degree Celsius. It is represented by the symbol \( c \) and measured in joules per kilogram per Kelvin (J/kgâ‹…K). In the context of the subway station scenario, we are particularly interested in the specific heat capacity of air because the heat generated from stopping the train is transferred to the air in the station. This property is crucial in determining how much the temperature of the air will rise. The given specific heat capacity of air is 1020 J/kgâ‹…K. This means for every kilogram of air, 1020 joules of energy is needed to increase its temperature by one Kelvin. Knowing the specific heat capacity allows us to calculate the temperature change by utilizing the relationship:- \( Q = mc\Delta T \), where \( Q \) is the heat absorbed, \( m \) is mass, \( c \) is specific heat capacity, and \( \Delta T \) is the temperature change. Utilizing specific heat capacity helps us figure out the relationship between the energy change and the temperature variation in this problem.

Heat transfer is the process by which heat energy is exchanged between physical systems. In our subway problem, heat transfer occurs when the kinetic energy of the moving train is converted into heat energy by the brakes. This heat is then distributed uniformly to the air in the subway station.The total heat energy transferred, \( Q \), equals the initial kinetic energy of the train. To find out how this affects the air temperature in the station, follow these steps:

• First, calculate the volume of the station from its dimensions: 65.0 m long, 20.0 m wide, and 12.0 m high, yielding \(65.0 \times 20.0 \times 12.0 = 15600 \text{ m}^3\).
• Using the density of air, \( \rho = 1.20 \text{ kg/m}^3\), calculate the mass of the air: \( m = 1.20 \times 15600\).
• Apply the formula \( Q = mc\Delta T \) to find \( \Delta T \), where \( Q \) is the total heat from kinetic energy, and \( c \) is the specific heat capacity (1020 J/kgâ‹…K).

Understanding heat transfer in this context helps to determine quantitatively how the energy conversion affects the air temperature, which is the problem's requirement.