Aclosed, rigid tank fitted with a paddle wheel contains 2 kg of air, initially at 300 k. during an interval of 5 minutes, the paddle wheel transfers energy to the air at a rate of 1 kw. during the interval, the air also receives energy by heat transfer at a rate of .5 kw. these are the only energy transfers. assuming the ideal gas model for the air, and no overall changes in kinetic or potential energy, determine the final temperature of the air, in k.

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.

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explanation: