inside the cylinder. Considera fire extinguisher containing 0.1 m3 of CO2 initially at 20 MPa and 300 K. Assume that CO2is an ideal gas with ? CP = 29 J/(mol K). The valve on the extinguisher can be modeled as anideal orifice with molar flow rate given byn? = C0a0f(?)?PT, (1)where C0 = 0.8 is the orifice coefficient, a0 = 10?3 m2 is the orifice area, ?P is the differencebetween the pressure in the cylinder and the ambient pressure, and f(?) = 0.5 mol K/s Pam2 is the heat capacity function. Assuming that heat transfer to the cylinder is negligible,develop an expression for the gas pressure in the cylinder as a function of time.(a) At what time will the pressure in the cylinder be 5 bar?(b) What will the temperature of the gas in the cylinder be at that time?(c) Make plots of P versus t and T versus t.
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