Concept explainers
The final temperature in the balloon.
Answer to Problem 127P
The final temperature in the balloon is
Explanation of Solution
Write the equation of mass balance.
Here, the inlet mass is
The change in mass of the system for the control volume is expressed as,
Here, the suffixes 1 and 2 indicates the initial and final states of the system.
Consider the given balloon as the control volume. Initially the balloon is filled with helium and connected to the supply line with the valve, the valve is opened, and helium is allowed to enter the balloon until it reaches the pressure of supply line. No mass is allowed to exit the balloon i.e.
Rewrite the Equation (I) as follows.
Write the formula for initial and final masses.
Here, the pressure is
Write the pressure and volume relation as follows.
Write the energy balance equation.
Here, the heat transfer is
The balloon expands when further helium is filled and the boundary work is done. i.e.
The Equation (VI) reduced as follows.
Write the general formula for boundary work by the helium (expansion of balloon).
Write the general expressions for enthalpy and internal energy.
Here, the specific heat at constant pressure is
Rewrite the equation (VII) as follows with reference to the general expression of enthalpy and internal energy.
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The gas constant
Refer Table A-2 (a), “Ideal-gas specific heats of various common gases”.
The specific heat at constant pressure
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the final temperature in the balloon is
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Chapter 5 Solutions
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