To calculate the volume of gas in the diver's blood at a different pressure, we can use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume, given a constant temperature. The mathematical representation of Boyle's Law is:
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \( P_1 \) = initial pressure (250 atm)
- \( V_1 \) = initial volume (0.04 L)
- \( P_2 \) = final pressure (50 atm)
- \( V_2 \) = final volume (unknown)
We can rearrange this equation to solve for \( V_2 \):
\[ V_2 = \frac{P_1 V_1}{P_2} \]
Now plug in the values:
\[ V_2 = \frac{250 , \text{atm} \times 0.04 , \text{L}}{50 , \text{atm}} \]
Calculating this gives:
\[ V_2 = \frac{10}{50} \] \[ V_2 = 0.2 , \text{L} \]
Thus, the volume of the gas in the diver's blood when the pressure is 50 atmospheres is 0.2 liters.
2 answers