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# hw9 - C HAPTER 21 HEAT WORK AND T HE FIRST LAW O F...

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CHAPTER 21 HEAT, WORK, AND THE FIRST LAW OF THERMODYNAMICS ActivPhysics can help with these problems: Activities 8.5-8.13 Section 21-1: The First Law of Thermodynamics Problem 1. In a perfectly insulated container, 1.0 kg of water is stirred vigorously until its temperature rises by 7.0°C. How much work was done on the water? Solution Since the container is perfectly insulated thermally, no heat enters or leaves the water in it. Thus, Q = 0 in Equation 21-1. The change in the internal energy of the water is determined from its temperature rise, AU = rnc AT (see comments in Section 19-4 on internal energy), so W = -AW = -(1 kg) x (4.184 kJ/kg.K)(7 K) = -29.3 kJ. (The negative sign signifies that work was done on the water.) Problem 5. The most efficient large-scale electric power generating systems use high-temperature gas turbines and a so-called combined cycle system that maximizes the conversion of thermal energy into useful work. One such plant produces electrical energy at the rate of 360 hlW, while extracting energy-from its natural gas fuel at the rate of 670 MW. (a) At what rate does it reject waste heat to the environment? (b) Find its efficiency, defined as the percent of the total energy extracted from the fuel that ends up as work. Solution (a) If we assume that the generating system operates in a cycle and choose it as "the system," then dli/dt = 0 and Equation 21-2 implies dQ/dt = dW/dt. Here, dW/dt is the rate that the generator supplies energy to its surroundings (360 h/lW in this problem) and dQ/dt is the net rate of heat flow into the generator from the surroundings. Since the system is just the generator, the net heat flow is the difference between

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