Answer:
The final temperature of the air is
Explanation:
We can start by doing an energy balance for the closed system
where
= the change in kinetic energy.
= the change in potential energy.
= the total internal energy change in a system.
Q = the heat transferred to the system.
W = the work done by the system.
We know that there are no changes in kinetic or potential energy, so and
and our energy balance equation is
We also know that the paddle-wheel transfers energy to the air at a rate of 1 kW and the system receives energy by heat transfer at a rate of 0.5 kW, for 5 minutes.
We use this information to calculate the total internal energy change using the energy balance equation.
We convert the interval of time to seconds
We can use the change in specific internal energy to find the final temperature of the air.
We are given that and the air can be describe by ideal gas model, so we can use the ideal gas tables for air to determine the initial specific internal energy
Next, we will calculate the final specific internal energy
With the value and the ideal gas tables for air we make a regression between the values
and
and we find that the final temperature
is 605 K.
