Explanation Assume the kinetic and potential energy changes as negligible. The system of tank and the valve is taken as the control volume for analysis. The figure below shows the control volume for the system. Figure-(1) Write the mass rate balance equation. d m c v d t = m ˙ i d m c v = m ˙ i ⋅ d t (I) Here, the change in mass of the control volume is d m c v and the rate of mass flow rate at inlet is m ˙ i . Integrate the above Equation. ∫ 1 2 d m c v = ∫ m ˙ i ⋅ d t m 2 − m 1 = m (II) Here, the mass at initial state is m 1 , the mass at final state is m 2 and the mass added to the tank is m . Write the initial mass in the tank. m 1 = V v 1 (III) Here, the specific volume at the initial state is v 1 and the volume of the tank is V . Substitute V v 1 for m 1 in Equation (II). m 2 − V v 1 = m m 2 = V v 1 + m (IV) Write the specific volume at final state. v 2 = V m 2 (V) Write the steady state equation for the control volume. d U c v d t + W ˙ c v + H ˙ e = Q ˙ c v + H ˙ i d U c v d t + W ˙ c v = Q ˙ c v + ( H ˙ i − H ˙ e ) (VI) Here, the rate of change of internal energy of the control volume is d U c v d t , the rate of work flow through the control volume is W ˙ c v , the rate of heat transfer through the control volume is Q ˙ c v , the rate of enthalpy at inlet is H ˙ i and the rate of enthalpy at exit is H ˙ e . There is no work flow through the control volume hence, W ˙ c v = 0 . There is no flow of enthalpy from exit hence, H ˙ e = 0 . Write the rate of enthalpy at inlet. H ˙ i = m ˙ i h i Write the change in internal energy for the control volume. Δ U c v = m 2 u 2 − m 1 u 1 Here, the specific internal energy at initial state is u 1 and the specific internal energy at final state is u 2 Substitute m i h i for H ˙ i , 0 for H ˙ e , 0 for W ˙ c v in Equation (VI). ( d U c v ) d t + 0 = Q ˙ c v + ( m ˙ i h i − 0 ) d U c v = Q ˙ c v ⋅ d t + m ˙ i h i ⋅ d t (VII) Integrate the above expression. Δ U c v = ∫ Q ˙ c v ⋅ d t + ∫ m ˙ i h i ⋅ d t = Q + h i ( m 2 − m 1 ) (VIII) Substitute m 2 u 2 − m 1 u 1 for Δ U c v in Equation (VIII)

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118412930

Author: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey

Publisher: WILEY

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Chapter 4.12, Problem 116P

To determine

The specific volume in ft3/lb at the final state of the control volume.

The magnitude of heat transfer between the tank and the surrounding in Btu.

The direction of heat transfer between the tank and the surrounding.

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Chapter 4.12, Problem 115P

Chapter 4.12, Problem 117P

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The specific volume in ft 3 / lb at the final state of the control volume. The magnitude of heat transfer between the tank and the surrounding in Btu . The direction of heat transfer between the tank and the surrounding.

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The specific volume in ft3/lb at the final state of the control volume. The magnitude of heat transfer between the tank and the surrounding in Btu. The direction of heat transfer between the tank and the surrounding.

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Chapter 4 Solutions

The specific volume in ft3/lb at the final state of the control volume.

The magnitude of heat transfer between the tank and the surrounding in Btu.

The direction of heat transfer between the tank and the surrounding.