# Figure P4.67 illustrates a system and fixed control volume attime t and the system at a

**Chapter 4, Problem 4.67**

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Figure P4.67 illustrates a system and fixed control volume attime t and the system at a short time t later. The system temperatureis T = 100 F at time t and T = 103 F at time t + t, wheret = 0.1 s. The system mass, m, is 2.0 slugs, and 10 percent ofit moves out of the control volume in t = 0.1 s. The energy perunit mass u is cvT, where cv = 32.0 Btu/slug F. The energy Uof the system at any time t is mu. Use the system or Lagrangianapproach to evaluate DU/Dt of the system. Compare this resultwith the DU/Dt evaluated with that of the material time derivativeand flux terms.

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