An ideal gas undergoes a cyclic process abcda which is shown by pressure-density curve.
Then,
A
work done by the gas in process bc is zero
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B
work done by the gas in the process cd is negative
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C
internal energy of the gas at point 'a' is greater than the internal energy at point 'c'
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D
net work done by the gas in the cycle is negative
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Solution
The correct option is D net work done by the gas in the cycle is negative P=ρM0RT⇒Pρ=RM0TSlopeofthecurveisproportionaltotemperatureHence,cdandabareisothermalprocesses.Asρ∝1V,bcanddaareisochoricprocesses.
Since is no change of volume during process bc, the work done is zero.
Area under the curve cd gives the work done, and volume is decreasing. So, work done is negative.
Net work done is negative, from the PV diagram (because the arrows are anticlockwise)
Internal energy is proportional to temperature. Since ab is an isothermal process, we can compare temperature at c and b. Ta=Tb<Tc⟹Ua<Uc