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  • A vertical cylinder pistion system has cross-section S. It contains 1 mole of an ideal monoatomic gas under a pistion of mass M. At a certain instant a heater is switched on which transmits a heat

A vertical cylinder pistion system has cross-section S. It contains 1 mole of an ideal monoatomic gas under a pistion of mass M. At a certain instant a heater is switched on which transmits a heat q per unit time ot the cylinder. Find the velocity v of the pistion under the condition that pressure under the pistionis constant and the system is thermally insulated.

Option: 1

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Option: 2

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Option: 3

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Option: 4

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Answers (1)

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\mathrm{Gas \: pressure =P_{0}+\frac{M g}{S}, Where \: M\text{is mass of the position}}
\operatorname{As~}_{\mathrm{v}}=\frac{3}{2} \mathrm{R}
\therefore \Delta \mathrm{U}=\frac{3}{2} \mathrm{R} \Delta \mathrm{T}=\frac{3}{2} \mathrm{P} \Delta \mathrm{V}
\mathrm{Q}=\mathrm{P} \Delta \mathrm{V}+\Delta \mathrm{U}=\mathrm{P} \Delta \mathrm{V}+\frac{3}{2} \mathrm{P} \Delta \mathrm{V}=\frac{5}{2} \mathrm{P} \Delta \mathrm{V}
\Delta \mathrm{V}=\mathrm{Sdx}

or \: \mathrm{Q}=\mathrm{q} \cdot \mathrm{dt}=\frac{5}{2} \mathrm{PSdx}
or \: \frac{d x}{d t}=\frac{2 q}{5 P S}=\frac{2 q}{5\left(P_{0}+\frac{M g}{S}\right) S}

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