Numerade

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INSTANT ANSWER

A piston-cylinder assembly contains 2 lb of water initially at 100 lbf/in2 and 400°F. The water undergoes two processes in series: a constant-pressure process followed by a constant -volume process. At the end of the constant-volume process, the temperature is 300°F and the water is a two-phase liquid-vapor mixture with a quality of 60%. Neglect kinetic and potential energy effects. a) Sketch T-v diagram b) Sketch p-v diagram c) Label states with their p, v, and T values d) Identify where work is done on or by the system on the diagram. Indicate whether it is done on or by the system. e) Determine the work and heat transfer for each process in Btu.

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INSTANT ANSWER

A gas within a piston–cylinder assembly undergoes a thermodynamic cycle consisting of three processes in series, beginning at state 1 where m = 0.5 kg, p1 = 1 bar, V1 = 1.5 m3, as follows: Process 1–2: Compression with pV = constant, W12 = -102 kJ, u1 = 424 kJ/kg, u2 = 780 kJ/kg. Process 2–3: W23 = 0, Q23 = -150 kJ. Process 3–1: W31 = 48 kJ. There are no changes in kinetic or potential energy. Determine Q12 and Q31, each in kJ.

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ANSWERED

Christopher Dzorkpata

Numerade educator

Find the power series solution of the given differential equation y''-xy'=e^-x

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ANSWERED

Linda Hand

Numerade educator

Find the power series solution of the given initial-value problem y''-xy=0, y(0)=1, y'(0)=-1

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ANSWERED

Christopher Dzorkpata

Numerade educator

Find the general solution if the given differential equation by using the variation of parameters method. y'''+y'=2sinx-cscx, 0<x<pi/2

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INSTANT ANSWER

Find the general solution if the given differential equation by using the variation of parameters method. y'''+y'=2tanx, -pi/2<x<pi/2

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ANSWERED

Naresh Bagrecha

Numerade educator

Find the general solution of the given initial value problem. y''' - y'' + y' - y = 0; y(0) = 2, y'(0) = -1, y''(0) = -2

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INSTANT ANSWER

Verify that \( y_{1}=x \) and \( y_{2}=x e^{x} \) are solutions of the differential equation \[ x^{2} y \prime \prime-x(x+2) y \prime+(x+2) y=0 ; \quad x>0 \] Do they constitute a fundamental set of solutions?

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ANSWERED

Christopher Dzorkpata

Numerade educator

Use the the method of reduction of order to find the second solution of the given differential equation on the given interval I. x^{2}y'' - 2xy' + (2 - x^{2})y = 0; y_{1} = xe^{x}, I : x > 0

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INSTANT ANSWER

Find the arc length parameter along the curve from the point where \( \mathrm{t}=0 \) by evaluating the integral \( \mathrm{s}=\int|\mathbf{v}| \mathrm{d} \tau \). Then find the length of the indicated portion of the curve. \[ r(t)=\left(2 e^{t} \cos t\right) i+\left(2 e^{t} \sin t\right) j+2 e^{t} k, \quad-\ln 4 \leq t \leq 0 \] The arc length parameter is \( \mathrm{s}(\mathrm{t})=2 \sqrt{3} e^{\mathrm{t}}-2 \sqrt{3} \). (Type an exact answer, using radicals as needed.) The length of the indicated portion of the curve is \( \square \) units. (Type an exact answer, using radicals as needed.)

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Benjamin J.