A balloon is filled with helium at sea level. The volume was measured to be 3.1 liters at a pressure of 0.97 atmosphere. If the balloon is released ,it drifts upward. At a height of 4 kilometers, the pressure is measured to be 0.61 atmospheres. What is the volume of the balloon? square

To solve this problem, we can use the ideal gas law in the form of Boyle's Law, which states that for a given amount of gas at constant temperature, the pressure and volume are inversely proportional. Mathematically, this is expressed as:<br /><br />\[ P_1 V_1 = P_2 V_2 \]<br /><br />where:<br />- \( P_1 \) is the initial pressure,<br />- \( V_1 \) is the initial volume,<br />- \( P_2 \) is the final pressure,<br />- \( V_2 \) is the final volume.<br /><br />Given:<br />- \( P_1 = 0.97 \) atm,<br />- \( V_1 = 3.1 \) liters,<br />- \( P_2 = 0.61 \) atm.<br /><br />We need to find \( V_2 \).<br /><br />Using Boyle's Law:<br /><br />\[ 0.97 \times 3.1 = 0.61 \times V_2 \]<br /><br />Solving for \( V_2 \):<br /><br />\[ V_2 = \frac{0.97 \times 3.1}{0.61} \]<br /><br />\[ V_2 = \frac{3.007}{0.61} \]<br /><br />\[ V_2 \approx 4.93 \text{ liters} \]<br /><br />Therefore, the volume of the balloon at a height of 4 kilometers is approximately 4.93 liters.