Complete Question
The complete question is shown on the first uploaded image
Answer:
The expression for the change in the air temperature is [tex]\Delta T = \frac{Mv^2}{2 \rho_{air} c_{air}* V}[/tex]
Explanation:
From the question we are told that
The mass of the train is M
The speed of the train is v
The volume of the station is V
The density of air in the station is [tex]\rho_{air}[/tex]
The specific heat of air is [tex]c_{air}[/tex]
The workdone by the break can be mathematically represented as
[tex]W =\Delta KE = \frac{1}{2} Mv^2[/tex]
Now this is equivalent to the heat transferred to air in the station
Now the heat capacity of the air in the station is mathematically represented as
[tex]Q = \rho_{air} * m_{air} * c_{air} (\Delta T)[/tex]
Now Since this is equivalent to the workdone by the breaks we have that
[tex]\frac{1}{2} Mv^2 = m_{air} * c_{air} (\Delta T)[/tex]
=> [tex]\Delta T = \frac{Mv^2}{2 \rho_{air} c_{air}* V}[/tex]
