Edits to “Statement”, “Answer”
en/5.5.12.md
+2 −2
| @@ -1,6 +1,6 @@ | |||
| ### Statement | |||
| − | $5.5.12.$ | ||
| + | $5.5.12.$ In how many strokes of a piston pump with a working volume $V$ can the pressure in a vessel of capacity $V_0$ be lowered from atmospheric $P_0$ to $P$? | ||
| ### Solution | |||
| Everty time the pump is connected to the container and the piston is pulled, the volume of the gas increases from $V_0$ to $V_0+V$, and its pressure becomes $V_0/(V_0+V)$ of its former value (assuming constant temperature). In order for the pressure of the gass to drop from $P_0$ to $P$, we must apply $n$ strokes of the pump so that | |||
| \[\left(\frac{V_0}{V_0+V}\right)^n=\frac{P}{P_0}\quad\Rightarrow\quad n=\frac{\ln(P_0/P)}{\ln(1+V/V_0)}.\] | |||
| @@ -10,4 +10,4 @@Solution | |||
| #### Answer | |||
| − | [Insert a concise answer or boxed result] | ||
| + | $\frac{\ln(P_0/P)}{\ln(1+V/V_0)}$ | ||
| @@ -1,6 +1,6 @@ | |||
| ### Statement | ### Statement | ||
| $5.5.12.$ |
$5.5.12.$ In how many strokes of a piston pump with a working volume $V$ can the pressure in a vessel of capacity $V_0$ be lowered from atmospheric $P_0$ to $P$? | ||
| ### Solution | ### Solution | ||
| Everty time the pump is connected to the container and the piston is pulled, the volume of the gas increases from $V_0$ to $V_0+V$, and its pressure becomes $V_0/(V_0+V)$ of its former value (assuming constant temperature). In order for the pressure of the gass to drop from $P_0$ to $P$, we must apply $n$ strokes of the pump so that | Everty time the pump is connected to the container and the piston is pulled, the volume of the gas increases from $V_0$ to $V_0+V$, and its pressure becomes $V_0/(V_0+V)$ of its former value (assuming constant temperature). In order for the pressure of the gass to drop from $P_0$ to $P$, we must apply $n$ strokes of the pump so that | ||
| \[\left(\frac{V_0}{V_0+V}\right)^n=\frac{P}{P_0}\quad\Rightarrow\quad n=\frac{\ln(P_0/P)}{\ln(1+V/V_0)}.\] | \[\left(\frac{V_0}{V_0+V}\right)^n=\frac{P}{P_0}\quad\Rightarrow\quad n=\frac{\ln(P_0/P)}{\ln(1+V/V_0)}.\] | ||
| @@ -10,4 +10,4 @@Solution | |||
| #### Answer | #### Answer | ||
| [Insert a concise answer or boxed result] | $\frac{\ln(P_0/P)}{\ln(1+V/V_0)}$ | ||