A balloon is filled to a volume of 2.20 L at a temperature of 25.0 ⁰C. The balloon is then heated to a temperature of 51.0 ⁰C. find the new volume of the balloon.
Answer (1)
[tex]\begin{gathered}\begin{gathered}{\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} \\\end{gathered}\end{gathered}[/tex] To find the new volume of the balloon after it is heated, we can use Charles's Law. This law states that the volume of a gas is directly proportional to its temperature when the pressure is constant. Charles's Law can be expressed mathematically as: [tex]\frac{V_1}{T_1} = \frac{V_2}{T_2}[/tex] Where: [tex]V_1[/tex] = initial volume of the gas (2.20 L)[tex]T_1[/tex] = initial temperature in Kelvin[tex]V_2[/tex] = new volume of the gas [tex]T_2[/tex] = new temperature in Kelvin Convert temperatures to Kelvin We need to convert the temperatures from Celsius to Kelvin using the formula: [tex]T(K) = T(^\circ C) + 273.15[/tex] For the initial temperature: [tex]T_1 = 25.0 + 273.15 = 298.15 \text{ K}[/tex] For the new temperature: [tex]T_2 = 51.0 + 273.15 = 324.15 \text{ K}[/tex] Use Charles's Law to find V₂ Now we can substitute the known values into Charles's Law: [tex]\frac{2.20 \text{ L}}{298.15 \text{ K}} = \frac{V_2}{324.15 \text{ K}}[/tex] Cross-multiply to solve for V₂ Cross-multiplying gives us: [tex]V_2 = 2.20 \text{ L} \times \frac{324.15 \text{ K}}{298.15 \text{ K}}[/tex] Calculate V₂ Now we can calculate [tex]V_2[/tex]: [tex]V_2 \approx 2.20 \text{ L} \times 1.087 = 2.39 \text{ L}[/tex] Conclusion Therefore, the new volume of the balloon when heated to 51.0 °C is approximately 2.39 L.
