Question

Hi! Could you please explain the solution to me step by step?

At a party some balloons are filled with helium. To fill them they have used gas from a bottle with volume 45 dm^3 and the pressure 1.00 MPa. The balloons are made to hold a pressure of 150 kPa. How many such balloons you can inflate if the balloons have an average volume of 4.0 dm^3?

Answer 1

Question #36084

Hi! Could you please explain the solution to me step by step?

At a party some balloons are filled with helium. To fill them they have used gas from a bottle with volume 45 dm³ and the pressure 1.00 MPa. The balloons are made to hold a pressure of 150 kPa. How many such balloons you can inflate if the balloons have an average volume of 4.0 dm³?

Solution:

Let

$$V_{\text{bottle}} = 45 \, \text{L}$$ $$P_{\text{bottle}} = 1.00 \, \text{MPa} = 1000 \, \text{kPa}$$ $$V_{\text{balloons}} = 4 \, \text{L}$$ $$P_{\text{balloons}} = 150 \, \text{kPa}$$ $$N_{\text{balloons}} = ?$$

According to the Boyle's law (isothermal process)

$V_{\text{bottle}} P_{\text{bottle}} = P_{\text{balloons}} V_{\text{total}}$ were $V_{\text{total}}$ is the total volume of the helium after inflating balloons. Such as after inflating the balloons in bottle is the helium too

$$V_{\text{total}} = N_{\text{balloons}} V_{\text{balloons}} + V_{\text{bottle}}$$ $$V_{\text{bottle}} P_{\text{bottle}} = P_{\text{balloons}} (N_{\text{balloons}} V_{\text{balloons}} + V_{\text{bottle}})$$ $$N_{\text{balloons}} = \frac{\frac{V_{\text{bottle}} P_{\text{bottle}}}{P_{\text{balloons}}} V_{\text{bottle}}}{V_{\text{balloons}}}$$ $$N_{\text{balloons}} = \frac{\frac{45 \cdot 1000}{150} \cdot 45}{4} = 63.75$$

Such as the number of the balloons must be integer

Answer: 63 balloons.