Calculate the decrease in tempareture when 2.00 L At 20.0 °C is compressed to 1.00 L.
Answer (1)
[tex]\begin{gathered}\begin{gathered}{\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} \\\end{gathered}\end{gathered}[/tex] To calculate the decrease in temperature when a gas is compressed from 2.00 L at 20.0 °C to 1.00 L, we can use the Ideal Gas Law and Charles's Law. Understand Charles's Law Charles's Law states that the volume of a gas is directly proportional to its temperature (in Kelvin) when pressure is held constant: [tex]\frac{V_1}{T_1} = \frac{V_2}{T_2}[/tex] where: [tex]V_1[/tex] is the initial volume, [tex]T_1[/tex] is the initial temperature (in Kelvin), [tex]V_2[/tex] is the final volume, [tex]T_2[/tex] is the final temperature (in Kelvin). Convert Initial Temperature to Kelvin The initial temperature is given in degrees Celsius. To convert this to Kelvin, we use the formula: [tex]T(K) = T(^\circ C) + 273.15[/tex] So, the initial temperature [tex]T_1[/tex] is: [tex]T_1 = 20.0 + 273.15 = 293.15 \text{ K}[/tex] Set Up the Equation Given: [tex]V_1 = 2.00 \text{ L}[/tex] [tex]V_2 = 1.00 \text{ L}[/tex] Using Charles's Law, we can set up the equation: [tex]\frac{2.00 \text{ L}}{293.15 \text{ K}} = \frac{1.00 \text{ L}}{T_2}[/tex] Solve for T₂ Rearranging the equation to find [tex]T_2[/tex]: [tex]T_2 = \frac{1.00 \text{ L} \cdot 293.15 \text{ K}}{2.00 \text{ L}} = \frac{293.15}{2} \approx 146.575 \text{ K}[/tex] Convert T₂ Back to Celsius To find the final temperature in Celsius: [tex]T_2 (^\circ C) = T_2 (K) - 273.15 = 146.575 - 273.15 \approx -126.575 ^\circ C[/tex] Calculate the Decrease in Temperature Now, we can calculate the decrease in temperature: [tex]\Delta T = T_1 - T_2 = 20.0 ^\circ C - (-126.575 ^\circ C) \approx 20.0 + 126.575 \approx 146.575 ^\circ C[/tex] Conclusion The decrease in temperature when 2.00 L of gas at 20.0 °C is compressed to 1.00 L is approximately: [tex]\Delta T \approx 146.58 ^\circ C[/tex] [tex]\sf\color{green}{⊱⋅ ────────────────────── ⋅⊰}[/tex][tex]\begin{gathered} \boxed{\begin{array}{cc} \sf \footnotesize \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ···\: ʚ\: \: \: \: \: \: Hope\:it\:helps \: \: \: \: \: ɞ \:··· \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\footnotesize\:\# CarryOnLearning \\ \sf\footnotesize ૮₍´˶ \: • \: . \: • \: ⑅ ₎ა \: \leadsto \footnotesize\sf\color{purple} \underline{Study\:Well!}\end{array}}\end{gathered}[/tex][tex]\sf\color{green}{⊱⋅ ────────────────────── ⋅⊰}[/tex][tex]\large\qquad\qquad\qquad\tt MARCH/14/2025 [/tex]
