Question 7.5.1: Capacitance of an Air Cylinder Obtain the capacitance of air...
Capacitance of an Air Cylinder
Obtain the capacitance of air in a rigid cylinder of volume 0.03 m³, if the cylinder is filled by an isothermal process. Assume the air is initially at room temperature, 293 K.
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The filling of the cylinder can be modeled as an isothermal process if it occurs slowly enough to allow heat transfer to occur between the air and its surroundings. In this case, n = 1 in the polytropic process equation, and from (7.5.6) we obtain,
C = \frac{m V}{np V} = \frac{V}{n R_{g} T} (7.5.6)
C = \frac{0.03}{1(287)(293)} = 3.57 × 10^{−7} kg · m^{2} /N
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