Concept explainers
A well-insulated 3-m × 4–m × 6-m room initially at 7°C is heated by the radiator of a steam heating system. The radiator has a volume of 15 L and is filled with superheated vapor at 200 kPa and 200°C. At this moment both the inlet and the exit valves to the radiator are closed. A 120-W fan is used to distribute the air in the room. The pressure of the steam is observed to drop to 100 kPa after 45 min as a result of heat transfer to the room. Assuming constant specific heats for air at room temperature, determine the average temperature of air in 45 min. Assume the air pressure in the room remains constant at 100 kPa.
FIGURE P4–136

The average temperature of air in 45 min.
Answer to Problem 136RP
The average temperature of air in 45 min is
Explanation of Solution
Show the free body diagram of the well-insulated room.
Write the expression for the energy balance equation.
Here, the total energy entering the system is
Substitute
Here, the mass is
From the Table (A-4 through A-6), obtain the value of specific volume, specific internal energy at the initial and the final states.
At initial pressure and temperature of
At final pressure of
Write the expression for final quality at the final state.
Here, the specific volume of saturated liquid is
Write the expression for final specific internal energy of a well-insulated room.
Here, the specific internal energy of saturated liquid is
Write the expression for total mass of a well-insulated room.
Here, the initial specific volume is
Write expression for the volume of the well-insulated room.
Write the expression of mass of air in a well-insulated room.
Here, the initial pressure is
Write the expression for amount of fan work done in 45 min.
Conclusion:
Here, the specific volume
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
For well-insulated room the energy balance equation.\
Substitute
Express the change in internal energy and boundary work into the constant pressure expansion and compression in Equation (IX).
Here, the rate of heat transfer entering is
Substitute
Therefore, the well-insulated room temperature rises from
Thus, the average temperature of air in 45 min is
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