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If the pressure of 200cm3 of a gas is halved at a constant temperature, what will be it's new volume
If the pressure of 200cm3 of a gas is halved at a constant temperature, what will be it's new volume
Answers
GPT-4o mini
According to Boyle's Law, the pressure of a gas is inversely proportional to its volume when temperature is held constant. This relationship can be expressed with the equation:
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \( P_1 \) is the initial pressure,
- \( V_1 \) is the initial volume,
- \( P_2 \) is the final pressure,
- \( V_2 \) is the final volume.
In this problem, the initial volume \( V_1 = 200 \, \text{cm}^3 \), and the pressure is halved, which means \( P_2 = \frac{1}{2} P_1 \).
Now we can substitute into the equation:
\[
P_1 \times V_1 = \left(\frac{1}{2} P_1\right) \times V_2
\]
Now, we can cancel \( P_1 \) on both sides (as long as \( P_1 \) is not zero):
\[
V_1 = \frac{1}{2} V_2
\]
Now, rearranging for \( V_2 \):
\[
V_2 = 2 \times V_1
\]
Substituting the value of \( V_1 \):
\[
V_2 = 2 \times 200 \, \text{cm}^3 = 400 \, \text{cm}^3
\]
Therefore, the new volume will be **400 cm³**.
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \( P_1 \) is the initial pressure,
- \( V_1 \) is the initial volume,
- \( P_2 \) is the final pressure,
- \( V_2 \) is the final volume.
In this problem, the initial volume \( V_1 = 200 \, \text{cm}^3 \), and the pressure is halved, which means \( P_2 = \frac{1}{2} P_1 \).
Now we can substitute into the equation:
\[
P_1 \times V_1 = \left(\frac{1}{2} P_1\right) \times V_2
\]
Now, we can cancel \( P_1 \) on both sides (as long as \( P_1 \) is not zero):
\[
V_1 = \frac{1}{2} V_2
\]
Now, rearranging for \( V_2 \):
\[
V_2 = 2 \times V_1
\]
Substituting the value of \( V_1 \):
\[
V_2 = 2 \times 200 \, \text{cm}^3 = 400 \, \text{cm}^3
\]
Therefore, the new volume will be **400 cm³**.