Edits to “Statement”, “Answer”
en/5.5.11.md
+2 −2
| @@ -1,11 +1,11 @@ | |||
| ### Statement | |||
| − | $5.5.11.$ [Insert the problem statement] | ||
| + | $5.5.11.$ How many strokes of a piston pump with a working volume $V$ can increase the pressure from atmospheric $P_0$ to $P$ in a vessel with a capacity of $V_0$? Ignore gas heating. | ||
| ### Solution | |||
| In order that the pressure of gas in a container with constant volume $V_0$ and temperature $T_0$ increases from atmospheric pressure $P_0$ to $P$, the number of moles of gas molecules must increase by $(P-P_0)V_0/(RT_0)$. Each stroke of the pump injects gas of volume $V$ at atmospheric pressure $P_0$ and temperature $T_0$, which has $P_0V/(RT_0)$ moles of gas molecules, into the container. Thus, the number of strokes required is $(P-P_0)V_0/(P_0V)$. | |||
| #### Answer | |||
| − | [Insert a concise answer or boxed result] | ||
| + | $\frac{(P-P_0)V_0}{P_0V}$ | ||
| @@ -1,11 +1,11 @@ | |||
| ### Statement | ### Statement | ||
| $5.5.11.$ [Insert the problem statement] | $5.5.11.$ How many strokes of a piston pump with a working volume $V$ can increase the pressure from atmospheric $P_0$ to $P$ in a vessel with a capacity of $V_0$? Ignore gas heating. | ||
| ### Solution | ### Solution | ||
| In order that the pressure of gas in a container with constant volume $V_0$ and temperature $T_0$ increases from atmospheric pressure $P_0$ to $P$, the number of moles of gas molecules must increase by $(P-P_0)V_0/(RT_0)$. Each stroke of the pump injects gas of volume $V$ at atmospheric pressure $P_0$ and temperature $T_0$, which has $P_0V/(RT_0)$ moles of gas molecules, into the container. Thus, the number of strokes required is $(P-P_0)V_0/(P_0V)$. | In order that the pressure of gas in a container with constant volume $V_0$ and temperature $T_0$ increases from atmospheric pressure $P_0$ to $P$, the number of moles of gas molecules must increase by $(P-P_0)V_0/(RT_0)$. Each stroke of the pump injects gas of volume $V$ at atmospheric pressure $P_0$ and temperature $T_0$, which has $P_0V/(RT_0)$ moles of gas molecules, into the container. Thus, the number of strokes required is $(P-P_0)V_0/(P_0V)$. | ||
| #### Answer | #### Answer | ||
| [Insert a concise answer or boxed result] | $\frac{(P-P_0)V_0}{P_0V}$ | ||