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Example: Electric resistive heaters are often used in houses to provide heat during winter

Example: Electric resistive heaters are often used in houses to provide heat during winter months. It consists of a simple duct with coiled resistance wires as shown. Consider a 20 kW heating system such that the air enters at 100 kPa and 17° C with a mass

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Example: Electric resistive heaters are often used in houses to provide heat during winter

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  1. Example: Electric resistive heaters are often used in houses to provide heat during winter months. It consists of a simple duct with coiled resistance wires as shown. Consider a 20 kW heating system such that the air enters at 100 kPa and 17° C with a mass flow rate of 1.8 kg/s. If it is known that the air leaves the duct with an exit temperature of 27° C (same pressure), determine the heat loss from the duct. Heat loss, dQ/dt=? To=17° C Assume: steady state, negligible KE and PE changes, air can be considered as idea gas To=27° C dEg/dt=20 kW where hout = Cp Tout and hin = Cp Tin From Table A-19 for air in YAC : Cp,out = Cp,in = 1.005 kJ/Kg.C <= total energy/heat going into the flowing air Hence, heat lost to the duct = 20 –18 = 2 kW

  2. Using a slightly different approach: Heat loss, dQ/dt=? To=17° C Again assume: 1.steady state 2. NegligibleKE and PE changes 3. Air can be considered as idea gas To=27° C dEg/dt=20 kW

  3. Recall that we wrote the First Law of Thermodynamics as: The above only applies for a STEADY FLOW process, I.e. a process where none of the properties inside the control Volume (C.V.), including energy, are changing with time. The turbine problem is an example of a steady process. If the process is unsteady, i.e. transient, the total amount of energy inside the system (or CV) can change. The First Law for such a process is given by: Where dECV/dt is the rate of change in the total energy of the Control Volume. First law-ex-1

  4. Transient Energy Balance (Unsteady State) Heat in q=dQ/dt E(t) not constant Work out dW/dt (4.19), p. 157 in Cengel’s book

  5. Example: Steam at a pressure of 2 MPa and a temperature of 350° C is exiting out from a tank through a valve to drive a turbine as shown. The exhausting steam enters an initially evacuated tank with a volume of 1 m3. The valve is closed when the second tank is filled with steam at a pressure of 1.4 MPa and a temperature of 500° C. Assume no significant heat transfer and KE and PE changes are also negligible. Determine the amount of work developed by the turbine. control volume to be analyzed V=1 m3 initially evacuated Steam 2 MPa 350 ° C Assumptions: dQ/dt=0 adiabatic process, KE and PE are negligible Steam properties at the first tank remains constant The second tank reaches final equilibrium after the filling process ends

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