Answer to Question #154684 in Mechanical Engineering for Ahmed A Mohammed

Question #154684

0.05 m^3 of gas at 6.9 bar expands reversibly in a Cylinder behind a piston according to a PV^ prime prime =C until the Volume is 0.08 m Calculate the work done by the gas and Sketch the process 0.05m ^ 3 of law on p-v diagram.


1
Expert's answer
2021-01-19T02:22:21-0500

From the above "PV^{2} =C" where C is constant

1 bar = "10^{5}N\/m^{2}"

from the above "p_{1}" = "6.9 \\times10^{5}N\/m^{2}"

Work done (W)=

"W=\\int_{v_{1}}^{v_{2}}p\\partial v"


"W=\\int_{v_{1}}^{v_{2}}\\frac{C}{v^{2}}\\partial v =C\\int_{v1}^{v2}\\frac{\\partial v}{v^{2}}\\\\\nC\\left [ \\frac{v^{-2+1}}{-2+1} \\right ] from\\ _{v_{2}}\\to v_{1}\\\\"

"C=\\left [ \\frac{1}{v_{1}}-\\frac{1}{v_{2}} \\right ]"

"C= pv^{2}=p_{1}v^{2}_{1}=6.9\\times10^{5}N\/m^{2}\\times0.05m^{2}"

=34500

Substituting the values of "v_{1},v_{2}" and C in the equation above we get

"W=34500 \\left [ \\frac{1}{0.05} -\\frac{1}{0.08}\\right ]N\/m"

Work done =258750 N/m

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