Answer to Question #256848 in Physics for freebandz

Question #256848

1) Derive the expression of workdone by the position on the cylinder in terms of the pressure and the volume of fluid in the cylinder

2) A unit of a fluid at a pressure of 3 bar and with a specific volume of 0.18m3/kg contained in a cylinder behind a piston that expands reversibly to a pressure of 0.6 bar the equation of pressure is taken as below p= c/v2 where c is a constant. Calculate the workdone during the process.


1
Expert's answer
2021-10-26T10:01:14-0400

1) The work is force times change in position caused by the action of the force, right?


W=FΔh.F=pA,W=F\Delta h.\\ F=pA,

where A - area:


W=pAΔh=pΔV.W=pA\Delta h=p\Delta V.

2) The work is


W=cv1v2dvv2=c(1v11v2).W=c\int^{v_2}_{v_1}\frac{dv}{v^2}=c\bigg(\frac1{v_1}-\frac1{v_2}\bigg).

Since the product of pressure and specific volume is constant:


c=p1v12=p2v22,c=30.182=0.0972 bar( m3/kg)2. v2=c/p2=0.0972/0.6=0.402 m3/kg.c=p_1v_1^2=p_2v_2^2,\\c=3·0.18^2=0.0972\text{ bar}·(\text{ m}^3/\text{kg})^2.\\\space\\ v_2=\sqrt{c/p^2}=\sqrt{0.0972/0.6}=0.402\text{ m}^3/\text{kg}.

Therefore:

W=0.0972105(10.1810.402)=29821 J.W=0.0972·10^5\bigg(\frac1{0.18}-\frac1{0.402}\bigg)=29821\text{ J}.


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