Refer to Example Problem 1.38, where for a 300-ft^3 oxygen tank compressed under a pressure of 500 psia and at a temperature of 40^◦ F, the density of the oxygen in the tank was determined to be 0.093 slug/ft^3 , and the weight of the oxygen in the tank was determined to be 897.385 lb. The oxygen

Question

Refer to Example Problem 1.38, where for a 300-[latex]ft^{3} [/latex] oxygen tank compressed under a pressure of 500 psia and at a temperature of [latex]40^{\circ } [/latex], the density of the oxygen in the tank was determined to be 0.093 slug/[latex]ft^{3} [/latex] , and the weight of the oxygen in the tank was determined to be 897.385 lb. The oxygen in the tank is further compressed under isothermal conditions (constant temperature) to a volume of 100 [latex]ft^{3} [/latex]. (a) Determine the resulting density of the oxygen in the tank. (b) Determine the resulting pressure of the oxygen in the tank. (c) Determine the resulting bulk modulus of elasticity of the oxygen in the tank.

Accepted Answer

(a) To determine the resulting density of the oxygen in the tank, one must note that the mass of the oxygen in Equation 1.33 [latex] ho =\frac{M}{V} [/latex], and thus, the weight of the oxygen Equation 1.44 [latex]\gamma =\frac{W}{V}=\frac{Mg}{V}= ho g[/latex] remains a constant as follows:

[latex] slug:=1lb\frac{sec^{2} }{ft} [/latex] [latex]P_{1} :=500psi=7.2 imes10^{4} psf[/latex] [latex]V_{1} =300ft^{3} [/latex]

[latex]g:=32.2\frac{ft}{sec^{2}} [/latex] [latex]P_{1} :=0.093 \frac{slug}{ft^{3} } [/latex] [latex]W_{1}:=897.385lb[/latex]

[latex]V_{2} =100ft^{3}[/latex] [latex]W_{2}:=W_{1}=897.385lb[/latex] [latex]\gamma _{2} :=\frac{W_{2}}{V_{2}} =8.974\frac{lb}{ft^{3}} [/latex]
[latex] ho _{2} :=\frac{\gamma_{2} }{g} =0.279\frac{slug}{ft^{3} } [/latex]

(b) Given compression under isothermal conditions (constant temperature), to determine the resulting pressure of the oxygen in the tank, one may apply Equation 1.155, [latex]\frac{p}{ ho } =C[/latex] as follows:

[latex]\frac{P_{1} }{ ho _{1}} =7.756 imes 10^{5} \frac{ft^{2} }{s^{2} } [/latex]

Guess value: [latex]P_{2}:=1psf[/latex]

Given

[latex]\frac{P_{1}}{ ho _{1}} =\frac{P_{2}}{ ho _{2}} [/latex]

[latex]P_{2}:=Find(P_{2})=2.157 imes 10^{5} psf[/latex]

(c) Given compression under isothermal conditions (constant temperature), the resulting bulk modulus of elasticity of the oxygen in the tank is equal to the absolute pressure of the oxygen in Equation 1.157 [latex]E_{\upsilon } =\frac{dp}{-\frac{dV}{V} } =\frac{dp}{\frac{d ho }{ ho } } = ho \frac{dp}{d ho } = ho \frac{d(C ho )}{d ho } =C ho \frac{d ho }{d ho} =C ho =p[/latex]. Thus:

[latex]E_{v} :=P_{2} imes 10^{5} psf [/latex]

Question 1.42: Refer to Example Problem 1.38, where for a 300-ft^3 oxygen t...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions