Edits to “Statement”, “Solution”, “Answer”
en/5.5.1.md
+1 −11
| @@ -1,11 +1,5 @@ | |||
| ### Statement | |||
| − | $5.5.1.$ [Insert the problem statement] | ||
| − | |||
| − | ### Solution | ||
| − | |||
| − | ### Problem | ||
| − | |||
| $5.5.1.$ The volume of a gas was halved, and its temperature was increased by a factor of $1.5$. By what factor did the gas pressure increase? | |||
| ### Solution | |||
| The amount of gas in this process remains constant, so for the two states (index 1 for the initial state, index 2 for the final state), we can write the ideal gas equation of state: | |||
| $$ | |||
| \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} | |||
| $$ | |||
| According to the problem statement, we are given: $V_2 = \frac{1}{2}V_1$ and $T_2 = \frac{3}{2}T_1$. | |||
| Substituting these into the equation: | |||
| $$ | |||
| \frac{P_1V_1}{T_1} = \frac{P_2 \cdot \frac{1}{2}V_1}{\frac{3}{2}T_1} | |||
| $$ | |||
| Hence: | |||
| $$ | |||
| @@ -30,10 +24,6 @@Solution | |||
| P_2 = 3P_1 | |||
| $$ | |||
| − | #### Answer: | ||
| − | |||
| − | By a factor of $3$ | ||
| − | |||
| #### Answer | |||
| − | |||
| + | By a factor of $3$ | ||
| @@ -1,11 +1,5 @@ | |||
| ### Statement | ### Statement | ||
| $5.5.1.$ [Insert the problem statement] | |||
| ### Solution | |||
| ### Problem | |||
| $5.5.1.$ The volume of a gas was halved, and its temperature was increased by a factor of $1.5$. By what factor did the gas pressure increase? | $5.5.1.$ The volume of a gas was halved, and its temperature was increased by a factor of $1.5$. By what factor did the gas pressure increase? | ||
| ### Solution | ### Solution | ||
| The amount of gas in this process remains constant, so for the two states (index 1 for the initial state, index 2 for the final state), we can write the ideal gas equation of state: | The amount of gas in this process remains constant, so for the two states (index 1 for the initial state, index 2 for the final state), we can write the ideal gas equation of state: | ||
| $$ | $$ | ||
| \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} | \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} | ||
| $$ | $$ | ||
| According to the problem statement, we are given: $V_2 = \frac{1}{2}V_1$ and $T_2 = \frac{3}{2}T_1$. | According to the problem statement, we are given: $V_2 = \frac{1}{2}V_1$ and $T_2 = \frac{3}{2}T_1$. | ||
| Substituting these into the equation: | Substituting these into the equation: | ||
| $$ | $$ | ||
| \frac{P_1V_1}{T_1} = \frac{P_2 \cdot \frac{1}{2}V_1}{\frac{3}{2}T_1} | \frac{P_1V_1}{T_1} = \frac{P_2 \cdot \frac{1}{2}V_1}{\frac{3}{2}T_1} | ||
| $$ | $$ | ||
| Hence: | Hence: | ||
| $$ | $$ | ||
| @@ -30,10 +24,6 @@Solution | |||
| P_2 = 3P_1 | P_2 = 3P_1 | ||
| $$ | $$ | ||
| #### Answer: | |||
| By a factor of $3$ | |||
| #### Answer | #### Answer | ||
| By a factor of $3$ | |||