To determine the pressure of the gas when the volume changes while keeping the temperature constant, we can use Boyle's Law. This law states that for a given mass of an ideal gas at a constant temperature, the pressure of the gas is inversely proportional to its volume. In mathematical terms, Boyle's Law is given by:
\(\[ P_1 \cdot V_1 = P_2 \cdot V_2 \]\)
Where:
- \(\( P_1 \)\) is the initial pressure of the gas.
- \(\( V_1 \)\) is the initial volume of the gas.
- \(\( P_2 \)\) is the final pressure of the gas.
- \(\( V_2 \)\) is the final volume of the gas.
Let's go through the problem step-by-step:
### Formula:
\(\[ P_1 \cdot V_1 = P_2 \cdot V_2 \]\)
### Input Numbers:
- Initial pressure (\(\( P_1 \)\)): 15 Pa
- Initial volume (\(\( V_1 \)\)): 5 mL
- Final volume (\(\( V_2 \)\)): 2 mL
- Temperature (\(\( T \)\)): 3 K (constant, and thus irrelevant for Boyle's Law)
### Solve for the final pressure (\(\( P_2 \)\)):
1. Rearrange the formula to solve for \(\( P_2 \)\):
\(\[ P_2 = \frac{P_1 \cdot V_1}{V_2} \]\)
2. Substitute the given values into the formula:
\(\[ P_2 = \frac{15 \, \text{Pa} \cdot 5 \, \text{mL}}{2 \, \text{mL}} \]\)
3. Calculate the result:
\(\[ P_2 = \frac{75 \, \text{Pa} \cdot \text{mL}}{2 \, \text{mL}} = 37.5 \, \text{Pa} \]\)
### Answer:
The pressure would be 37.5 Pa if the volume shrinks to 2 mL while the temperature remains at 3 K.
