Question

The pressure of a gas is 765 mm of Hg at 296 K. At what temperature will the pressure be 560 mm of Hg?

Answer 1

$\rm \large {\underbrace{\underline{\bigstar{Elucidation:-}}}}$

$\bf \blue {\underline{\underline{Given:}}}$

$\sf \to {Pressure(P_{1})=765mm}$

$\sf \to {Pressure(P_{2})=560mm}$

$\sf \to {Temperature(T_{1})=296k}$

$\bf \pink {\underline{\underline{To\: Find:}}}$

$\sf \to {Temperature(T_{2})=?}$

$\bf \purple {\underline{\underline{Work:}}}$

$\sf {According\: to\: Gay-Lussac's\:law}$ $\sf {(or)\: Charles\: 2^{nd}\: law,}$

$\sf {\boxed{Pressure∝Temperature}}$

$\sf {So\: a\: formula\: can\: be\: derived\: as,}$

$\sf \implies {\boxed{\frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}}}}$

$\large \sf \mapsto {\frac{765}{296}=\frac{560}{T_{2}}}$

$\large \sf \mapsto {T_{2}=\frac{560×296}{765}}$

$\sf {By\: solving,\: the\: answer\: comes\: out\: to\: be,}$

$\sf \implies {\boxed{T_{2}≃216k}}$

$\bf \orange {\underline{\underline{Henceforth:}}}$

$\sf {The\: Temprature\:comes\: out\: to\: be,}$ $\sf {216k\: or\: 57°c}$