Question
under the pressure of 250 atmospheres, a diver has 0.04 liter of gas in his blood. Calculate the volume of the gas in the diver's blood when the blood has a pressure of 50 atmospheres
Answers
GPT-4o mini
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**.
\[
P_1 V_1 = P_2 V_2
\]
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**.