Question

An LPG cylinder can withstand a pressure of 15 atm across its boundaries. If at room temp (300 K) it is filled with 2 atm pressure. Determine the temperature at which it will explode? (Options are in degree celsius)
(a) 216
(b) 2127
(c) 2400
(d) 27

Answer 1

Once filling is complete the mass, volume is fixed..

Now, as per Gay-lussac's Law :

Pressure and temperature of gas is directly proportional if the volume is kept constant.. i.e.

$\frac{p}{t} =k \: \: (given \: vol \: is \: constant)$

$Or,\: \frac{p1}{t1} = \frac{p2}{t2}</p><p>\\ Or,\: \frac{p1}{p2} = \frac{t1}{t2}</p><p>\\ Or,\: t2= \frac{p2}{p1} \times t1</p><p>\\</p><p>or,\:t2= \frac{15atm \times 300K}{2atm}=2250K = 1973C$

So, at 1973℃ pressure will be 15atm..

Hence it will explode at temp above this point.

Ans: (b) 2127

(However, 2127℃ represents 2400K, at which pressure will be 16atm.. i.e. cylinder would have been already exploded long before as 1atm pressure isn't negligible.. So, check ur question and option.. may be cylinder can withstand 16atm pressure.. and even if not ans would be same)