(a) Explanation Write the steady flow energy balance equation. d U d t + W ˙ + H ˙ e = Q ˙ + H ˙ i d U d t = Q ˙ − W ˙ + H ˙ i − H ˙ e (I) Here, the rate of heat transfer from the control volume is Q ˙ , the enthalpy rate at inlet of the control volume is H ˙ i , the enthalpy rate at the exit of the control volume is H ˙ e , the rate of change of internal energy is d U d t , and the rate of work flow through the control volume is W ˙ . Write the rate of enthalpy change for the control volume. H ˙ i − H ˙ e = m ˙ i h i − m ˙ e h e (II) Here, the mass flow rate at inlet is m ˙ i , the mass flow rate at exit is m ˙ e , the specific enthalpy at inlet is h i and the specific enthalpy at exit is h e . There is no work transfer hence rate of work flow through the control volume is zero, that is W ˙ = 0 . There is no flow of mass from exit hence, m ˙ e = 0 . Substitute 0 for m ˙ e in Equation (II). H ˙ i − H ˙ e = m ˙ i h i − 0 = m ˙ i h i Substitute m ˙ i h i for H ˙ i − H ˙ e , 0 for W ˙ in Equation (I). d U d t = Q ˙ − 0 + m ˙ i h i = Q ˙ + m ˙ i h i Integrate the above expression. Δ U = ∫ 1 2 Q ˙ ⋅ d t + ∫ 1 2 ( m ˙ i h i ) d t = Q + h i ∫ 1 2 m i ⋅ d t = Q + h i ( m ) 1 2 = Q + h i ( m 2 − m 1 ) (III) Here, the mass at initial state is m 1 , the mass at final state is m 2 and the heat transfer is Q . Write the change in internal energy. Δ U = m 2 u 2 − m 1 u 1 (IV) Here, the specific internal energy at initial state is u 1 and the specific internal energy at final state is u 2 . The tank is initially evacuated hence the enthalpy at initial state hence mass at initial sate is 0 and the internal energy at initial state is 0 hence, m 1 = 0 and u 1 = 0 (b) To determine The heat transfer between the tank contents and the surroundings in kJ .

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ISBN: 2818440116926

Author: MORAN

Publisher: WILEY CONS

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Chapter 4.12, Problem 110P

(a)

To determine

The final mass in the tank in g.

(b)

To determine

The heat transfer between the tank contents and the surroundings in kJ.

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Chapter 4.12, Problem 109P

Chapter 4.12, Problem 111P

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The final mass in the tank in g .