## College Physics (4th Edition)

The balloon would have a volume of $1313~m^3$
We can find an expression for the original volume: $P_1~V_1 = nRT_1$ $V_1 = \frac{nRT_1}{P_1}$ We can find an expression for the final volume: $P_2~V_2 = nRT_2$ $V_2 = \frac{nRT_2}{P_2}$ We can divide $V_2$ by $V_1$: $\frac{V_2}{V_1} = \frac{\frac{nRT_2}{P_2}}{\frac{nRT_1}{P_1}}$ $V_2 = \frac{P_1~T_2~V_1}{P_2~T_1}$ $V_2 = \frac{(1.00\times 10^5~N/m^2)(260~K)(5.0~m^3)}{(0.33\times 10^3~N/m^2)(300~K)}$ $V_2 = 1313~m^3$ The balloon would have a volume of $1313~m^3$.