Concept explainers
The initial rate of temperature rise of the air in the tank.
Answer to Problem 3.182P
The initial rate of temperature rise of the air in the tank is
Explanation of Solution
Given information:
The tank is insulated. The initial temperature inside the tank is
Write the expression for the unsteady flow energy equation for the control volume of the tank.
Here, the rate of the heat inlet to the control volume is
Since there is no energy interactions with the control volume so,
Since there is no mass leaving from the tank so,
Since the velocity at inlet and the datum are negligible.
Substitute
Write the expression for the energy stored by the control volume.
Here, the specific heat at constant volume is
Write the expression for the enthalpy.
Here, the enthalpy is
Write
Write the expression for the specific enthalpy.
Here, the specific heat at constant pressure is
Substitute
Write the expression for the mass flow rate at inlet with respect to time.
Substitute
Write the expression for the ideal gas equation.
Substitute
Calculation:
Convert the temperature from
Substitute
Conclusion:
The initial rate of temperature rise of the air in the tank is
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Chapter 3 Solutions
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