Question

Kindly answer it with a explanation :-)

#No spams

​

Answer 1

$\huge\sf\pink{Answer}$

☞ Temperature when it bursts will be 99.5° C

━━━━━━━━━━━━━

$\huge\sf\blue{Given}$

✭ $\sf P_1 = 12 \ atm$

✭ $\sf P_2 = 14.9 \ atm$

✭ $\sf T_1 = 27^{\circ} \ C$

━━━━━━━━━━━━━

$\huge\sf\gray{To \:Find}$

◈ Temperature in which the cylinder will explode?

━━━━━━━━━━━━━

$\huge\sf\purple{Steps}$

So as per the Gay lussaic's law,

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

Where

• P = Pressure
• T = Temperature
• Pressure ∝ Temperature

We shall first convet Temperature from Celcius to Kelvin,

➝ $\sf Kelvin = Celcius + 273$

➝ $\sf T_1 = 27^{\circ} + 273$

➝ $\sf \green{T_1 = 300 \ K}$

Substituting the given values in the given Question

➳ $\sf \dfrac{P_1}{T_1} = \dfrac{P_2}{T_2}$

➳ $\sf \dfrac{12}{300} = \dfrac{14.9}{T_2}$

«« Cross Multiply »»

➳ $\sf 12\times T_2 = 14.9\times 300$

➳ $\sf 12T_2 = 4470$

➳ $\sf T_2 = \dfrac{4470}{12}$

➳ $\sf \red{T_2 = 372.5 \ K}$

Now let's convet it back to Celcius,

»» $\sf Celcius = Kelvin - 273$

»» $\sf T_2 = 372.5-273$

»» $\sf \orange{T_2 = 99.5^{\circ} \ C}$

━━━━━━━━━━

☯ $\underline{\sf Let's \ Understand}$

⪼ At constant volume and and at constant number of moles, pressure is directly proportional to temperature

⪼ Gay lussac law is also called Charles second law

⪼ The pressure temperature graph at constant volume gives straight line

⪼ Gay lussaic's law was the basis for Avogadro's law

━━━━━━━━━━━━━━━━━━

Answer 2

$\bigstar\huge\boxed{\mathtt{\red{Solution:}}}$

As per the given question ,

• P 1 = 12 atm
• T 1 = 27 C

As per the ideal gas law formula the temperature must be in kelvin

Hence, in order to convert Celsius into kelvin add 273

T 1 = 273 +27 = 300 K

• P 2 = 14.9 atm ( amount of pressure the cylinder can withstand before exploding)

We need to find the temperature after the cylinder will explode

According to the ideal gas equation ,

$\implies\mathtt{\blue{PV=nRT }}$

Now as per the given condition V, n ,R are constant so ,

$\implies\mathtt{\dfrac{P}{T} =\dfrac{nR}{V} }$

$\implies\mathtt{\dfrac{P}{T} =const }$

Gay - Lussac's law states that when pressure is directly proportional to temperature when the volume becomes constant

Hence by using this law we can easily solve this question  ,

$\implies\mathtt{\orange{\dfrac{P_{1}}{T_{1}} = \dfrac{P_{2}}{T_{2} }}}$

$\implies\mathtt{T_{2} = \dfrac{P_{2}\times T_{1}}{ P_{1}}}$

$\implies\mathtt{T_{2} = \dfrac{14.9\times 300}{ 12}}$

$\implies\mathtt{T_{2} = \dfrac{4470}{ 12}}$

$\implies\mathtt{T_{2} = 372.5 K}$

$\implies\mathtt{T_{2} = 372.5 - 273 }$

$\implies\mathtt{\pink{T_{2} = 99.5 \: C }}$

The cylinder will explode at 99.5 C