Question

Um gás ideal está contido em um recipiente fechado, a volume constante, a uma temperatura de 27 °C. Para que a pressão desse gás se eleve de 2atm para 3atm, é necessário elevar a sua temperatura para quanto?

Answer 1

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⠀⠀⠀☞ Será necessário elevar sua temperatura para 177 [ºC]. ✅

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⠀⠀⠀⭐⠀Para realizar este exercício vamos utilizar a equação de Clapeyron.⠀⭐⠀

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                                   $\LARGE\red{\boxed{\pink{\boxed{\begin{array}{lcr}\green{\star}&&\green{\star}\\&\orange{\sf P \cdot v = n \cdot R \cdot T}&\\\green{\star}&&\green{\star}\\\end{array}}}}}$

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$\text{\Large\orange{ \diamond~~\bf P }~\pink{ \Longrightarrow }~}$ Pressão do gás em [atm] ⇒ (x [Pa] ≈ x · 10⁻⁵ [atm]);

$\text{\Large\orange{ \diamond~~\bf V }~\pink{ \Longrightarrow }~}$ Volume do gás em [m³] ⇒ (y [m³] = y · 10³ [L]);

$\text{\Large\orange{ \diamond~~\bf n }~\pink{ \Longrightarrow }~}$ Número de mols do gás;

$\text{\Large\orange{ \diamond~~\bf R }~\pink{ \Longrightarrow }~}$ Constante universal dos gases perfeitos ≈ 8,3 · 10⁻⁵ [m³·atm/K·mol];

$\text{\Large\orange{ \diamond~~\bf T }~\pink{ \Longrightarrow }~}$ Temperatura do gás em [K] ⇒ (z [K] = z - 273 [ºC] = (z - 273) · 1,8 + 32 [ºF]).

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⠀⠀⠀➡️⠀Sendo este um processo isocórico então temos:

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                            $\LARGE\gray{\boxed{\sf\orange{~~\begin{array}{c}\\\!\!\!\pink{\underline{\bf\quad Processo~isob\acute{a}rico\quad}}\!\!\!\\\\\\\blue{\sf \overbrace{\boxed{\normalsize\sf \dfrac{n \cdot R}{V}}}^{\sf constante} = \dfrac{P}{T}}\\\blue{\!\!\!\!\!\!\!\!\!\!\!\downarrow\!\!\searrow}\\\\\blue{\underbrace{\normalsize\sf \dfrac{n_{\scriptsize i} \cdot R}{V_{\scriptsize i}}} = \underbrace{\normalsize\sf \dfrac{n_{\scriptsize f} \cdot R}{V_{\scriptsize f}}}}\\\blue{\searrow\quad\;\;\swarrow}\\\\\blue{\boxed{\sf \dfrac{P_i}{T_i} = \dfrac{P_f}{T_f}}}\\\\\end{array}~~}}}$

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⌚ Hora da matemágica ✍

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                             $\Large\gray{\boxed{\sf~~\begin{array}{c}~\\\pink{\underline{~\underline{\text{\LARGE \bf\square\!\!\boxed{\subset}\boxed{\emptyset}\boxed{\eta}\boxed{\pi}\!\!\!^{^{\square}}\boxed{\alpha}\boxed{\ }\!_{\square} }}~}}\\\\\\\blue{\begin{cases}\sf~P_i =2 ~[atm]\\ \text{\large \sf~T_i = 27+273 = 300~[K] }\\ \sf~P_f =3~[atm] \\\sf~T_f =~?~[K]\end{cases}}\\\\\!\!\!\!\!\!\!\!^{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\!\!\!\!\!\!\!\!\\\orange{\bf \dfrac{P_i}{T_i} = \dfrac{P_f}{T_f}}\\\!\!\!\!\!\!\!\!^{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\!\!\!\!\!\!\!\!\\\blue{\sf \dfrac{2}{300} = \dfrac{3}{T_f}}\\\!\!\!\!\!\!\!\!^{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\!\!\!\!\!\!\!\!\\\blue{\sf T_f = \dfrac{300 \cdot 3}{2}}\\\!\!\!\!\!\!\!\!^{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\!\!\!\!\!\!\!\!\\\\\green{\boxed{\blue{\sf~T_f = 450~[K]}}~\checkmark}\\\\\end{array}~~}}$

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⠀⠀⠀⭐ Retornando a temperatura para [ºC] temos 450 - 273 = 177 [ºC]. ✌

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                                $\huge\green{\boxed{\rm~~~\gray{T_f}~\pink{=}~\blue{ 177~[^{\circ}C] }~~~}}$ ✅

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                             $\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

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⠀⠀⠀☀️ L͎̙͖͉̥̳͖̭̟͊̀̏͒͑̓͊͗̋̈́ͅeia mais sobre expansão isocórica:

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                                     https://brainly.com.br/tarefa/48944759 ✈  

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                                     $\huge\blue{\text{\bf\quad Bons~estudos.}}$ ☕

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                                          $\quad\qquad(\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios})$ ☄

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                             $\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }\LaTeX}$✍

                                $\sf(\purple{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly}$ ☘☀❄☃☂☻)

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                                                          $\Huge\green{\text{ \underline{\red{\mathbb{S}}\blue{\mathfrak{oli}}~}~\underline{\red{\mathbb{D}}\blue{\mathfrak{eo}}~}~\underline{\red{\mathbb{G}}\blue{\mathfrak{loria}}~} }}$ ✞

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