A thermocouple, with a spherical junction diameter of 0.5 mm, is used for measuring the temperature of hot air flow in a circular duct. The convection heat transfer coefficient of the air flow can be related with the diameter (D) of the spherical junction and the average air flow velocity (V) as h = 2.2(V/D)0.5, where D, h, and V are in m, W/m2?K and m/s, respectively. The properties of the thermocouple junction are k = 35 W/m?K, r = 8500 kg/m3, and cp = 320 J/kg?K. Determine the minimum air flow velocity that the thermocouple can be used, if the maximum response time of the thermocouple to register 99 percent of the initial temperature difference is 5 s.
Kinetic Theory of Gas
The Kinetic Theory of gases is a classical model of gases, according to which gases are composed of molecules/particles that are in random motion. While undergoing this random motion, kinetic energy in molecules can assume random velocity across all directions. It also says that the constituent particles/molecules undergo elastic collision, which means that the total kinetic energy remains constant before and after the collision. The average kinetic energy of the particles also determines the pressure of the gas.
P-V Diagram
A P-V diagram is a very important tool of the branch of physics known as thermodynamics, which is used to analyze the working and hence the efficiency of thermodynamic engines. As the name suggests, it is used to measure the changes in pressure (P) and volume (V) corresponding to the thermodynamic system under study. The P-V diagram is used as an indicator diagram to control the given thermodynamic system.
A thermocouple, with a spherical junction diameter
of 0.5 mm, is used for measuring the temperature of hot air
flow in a circular duct. The
of the air flow can be related with the diameter (D) of
the spherical junction and the average air flow velocity (V)
as h = 2.2(V/D)0.5, where D, h, and V are in m, W/m2?K
and m/s, respectively. The properties of the thermocouple
junction are k = 35 W/m?K, r = 8500 kg/m3, and cp =
320 J/kg?K. Determine the minimum air flow velocity that
the thermocouple can be used, if the maximum response
time of the thermocouple to register 99 percent of the initial
temperature difference is 5 s.
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