# Answer to Question #95480 in Electrical Engineering for Anthony

Question #95480
0.05m^3 of a gas at 6.9 bar expand reversibly in a cylinder behind a piston according to the law of pv^1.2=constant until the volume is 0.08m^3. Calculate the workdone by the gas and sketch the process on p-v diagram.
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2019-09-30T05:23:37-0400
1. Calculate the pressure when the gas expanded to 0.08 cubic meters:
"p_aV_a^{1.2}=p_bV_b^{1.2},\\\\\n\\space\\\\\np_b=p_a\\Bigg(\\frac{V_a}{V_b}\\Bigg)^{1.2}=3.926\\text{ bar, or }3.926\\cdot10^5\\text{ Pa}."

2. The work in the process is

"W=\\int_a^b pdV=\\int_a^b \\frac{\\text{const}}{V^{1.2}}dV=-\\int_a^b\\frac{\\text{const}}{0.2V^{0.2}}=\\\\\n\\space\\\\\n=-\\frac{\\text{const}}{0.2V_b^{0.2}}+\\frac{\\text{const}}{0.2V_a^{0.2}}=\\\\\n\\space\\\\\n=-\\frac{p_bV_b^{1.2}}{0.2V_b^{0.2}}+\\frac{p_aV_a^{1.2}}{0.2V_a^{0.2}}=\\frac{p_aV_a-p_bV_b}{0.2}=15476\\text{ J}."

3. The process on p-V diagram looks like Need a fast expert's response?

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