Question

a hot air balloon is filled to a volume of 44.5 l at 758 torr. what will be the volume of the balloon if the pressure decreases to 748 torr under constant temperature?
45.1 l
43.9 l
44.5 l
49.0 l

Explanation:

Step1: Recall Boyle's Law

Boyle's Law states that \(P_1V_1 = P_2V_2\) (at constant temperature), where \(P_1 = 758\) torr, \(V_1=44.5\) L, and \(P_2 = 748\) torr. We need to find \(V_2\).

Step2: Rearrange the formula to solve for \(V_2\)

From \(P_1V_1 = P_2V_2\), we can get \(V_2=\frac{P_1V_1}{P_2}\).

Step3: Substitute the values into the formula

Substitute \(P_1 = 758\), \(V_1 = 44.5\), and \(P_2=748\) into \(V_2=\frac{P_1V_1}{P_2}\), so \(V_2=\frac{758\times44.5}{748}\).
Calculate \(758\times44.5 = 758\times(40 + 4.5)=758\times40+758\times4.5=30320+3411 = 33731\).
Then \(V_2=\frac{33731}{748}\approx45.1\) L.

Answer:

45.1 L