Question

The pressure of a given mass of gas at 27 degree Celsius is 75 cm of mercury . The temperature in Celsius at which the pressure is doubled , the gas being heated at constant volume

Answer 1

Answer:

• The temperature (T) at which the pressure is Double is 327°C

Given:

$\boxed{\begin{minipage}{10 em} \textbf{\underline{Initial Conditions}}\colon \\\\ \bullet \rm P_1 = 75\;cm\;of\;Hg \\\bullet \rm T_1 = 27^\circ C\end{minipage}}\quad\boxed{\begin{minipage}{10 em}\textbf{\underline{Final Conditions}}\colon \\\\ \bullet \rm P_2 = 2\; P_1 \\\bullet \rm T_1 = \; ? \end{minipage}}$

Explanation:

$\rule{300}{1.5}$

From gay Lussac's law we Know,

$\large \bigstar \;\boxed{\tt P \propto T}$

$\mathfrak{Here}\begin{cases}\text{P Denotes Pressure} \\ \text{T Denotes Temperature}\end{cases}$

Now,

$\large\boxed{\tt P \propto T}$

$\displaystyle\dashrightarrow\tt \dfrac{P_1}{P_2}=\dfrac{T_1}{T_2} \\\\\\\dashrightarrow \tt \dfrac{P_1}{2\timesP_1}=\dfrac{27^\circ C}{T_2}\\\\\\\dashrightarrow \tt \dfrac{P_1}{2 \times P_1}=\dfrac{273+27\;K}{T_2}\\\\\\\dashrightarrow \tt \dfrac{1}{2} = \dfrac{300}{T_2}\\\\\\\dashrightarrow\tt T_2=2\times300\\\\\\\dashrightarrow\tt T_2=600\;K\\\\\\\dashrightarrow\tt T_2=(600-273)^\circ C \ \ \ \because [T_{(Celcius)}=T_{(Kelvin)}-273]$

$\dashrightarrow \large{\underline{\boxed{\red{\tt T_2 = 327\;^\circ C}}}}$

∴ The temperature (T) at which the pressure is Double is 327°C

$\rule{300}{1.5}$

Answer 2

$\huge \underline {\underline{ \mathfrak{ \green{Ans}wer \colon}}}$

_______________________________

$\boxed{\begin{minipage}{5cm}{\large\textbf{Initial Case}} \\\\ 1) Pressure (P_1) = 75 cm of Hg \\ 2) Temperature (T_1) = 75^{\circ} C \end{minipage}}$

$\boxed{\begin{minipage}{5cm}{\large\textbf{Final Case}} \\\\ 1) Pressure (P_2) = 2P_1 \\ 2) Temperature (T_2) = ? \end{minipage}}$

________________________________

From Gay Lussac's Law :

$\large{\boxed{\sf{\dfrac{P_1}{P_2} \: = \: \dfrac{T_1}{T_2}}}}$

$\implies {\sf{\dfrac{P_1}{2 \: \times \: P_1} \: = \: \dfrac{27^{\circ} C }{T_2}}}$

$\implies {\sf{\dfrac{1}{2} \: = \: \dfrac{(27 \: + \: 273) K}{T_2}}}$

$\implies {\sf{\dfrac{1}{2} \: = \: \dfrac{300}{T_2}}}$

$\implies {\sf{T_2 \: = \: 300 \: \times \: 2}}$

$\implies {\sf{T_2 \: = \: 600 \: K}}$