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Question Number 29490 by Victor31926 last updated on 09/Feb/18

$$\mathrm{A}\mathrm{gas}\mathrm{expands}\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{law}\mathrm{PV}=\mathrm{K}\left(\mathrm{constant}\right).$$$$\mathrm{Initialy},\mathbf{v}=1000\mathrm{cubic}\mathrm{metres}\mathrm{and}\mathbf{p}=40\mathrm{N}/{\mathrm{m}}^2.$$$$\mathrm{If}\mathrm{the}\mathrm{pressure}\mathrm{is}\mathrm{decreased}\mathrm{at}\mathrm{the}\mathrm{rate}\mathrm{of}5\mathrm{N}/{\mathrm{m}}^2/\min .\mathrm{find}\mathrm{the}\mathrm{rate}\mathrm{at}\mathrm{which}$$$$\mathrm{the}\mathrm{gas}\mathrm{is}\mathrm{expanding}\mathrm{when}\mathrm{its}\mathrm{volume}\mathrm{is}2000\mathrm{cubic}\mathrm{metres}.$$$$$$

Answered by Rasheed.Sindhi last updated on 09/Feb/18

$$\mathrm{PV}=\mathrm{K}$$$$\mathrm{When}\mathrm{V}=1000{\mathrm{m}}^3\mathrm{and}\mathrm{P}=40\mathrm{N}/{\mathrm{m}}^2$$$$\mathrm{K}=40\mathrm{N}/{\mathrm{m}}^2\times 1000{\mathrm{m}}^3=40000\mathrm{Nm}$$$$\mathrm{When}\mathrm{V}=2000{\mathrm{m}}^3$$$$\mathrm{P}=\frac{\mathrm{K}}{\mathrm{V}}=\frac{40000\mathrm{Nm}}{{2000\mathrm{m}}^3}=20\mathrm{N}/{\mathrm{m}}^2$$$$\mathrm{Per}\mathrm{minute}\mathrm{change}\mathrm{in}\mathrm{P},\mathrm{when}\mathrm{V}={2000\mathrm{m}}^3$$$$\mathrm{P}\mathrm{changes}\mathrm{from}20\mathrm{N}/{\mathrm{m}}^2\mathrm{to}15\mathrm{N}/{\mathrm{m}}^2$$$$\mathrm{Changed}\mathrm{volume}=\frac{\mathrm{K}}{\mathrm{Changed}\mathrm{pressure}}$$$$=\frac{40000\mathrm{Nm}}{15\mathrm{N}/{\mathrm{m}}^2}=2666\frac{2}{3}{\mathrm{m}}^3$$$$\mathrm{Change}\mathrm{in}\mathrm{volume}\left(\mathrm{in}\mathrm{one}\mathrm{minute}\right)$$$$=2666\frac{2}{3}{\mathrm{m}}^3-{2000\mathrm{m}}^3$$$$=666\frac{2}{3}{\mathrm{m}}^3/\min \left(\mathrm{expanding}\right)$$$$\mathrm{Please}\mathrm{confirm}\mathrm{the}\mathrm{answer}.$$

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