An iron cylinder contains helium at a pressure of 250 $k P a$ at 300 $K$ . The cylinder can withstand a pressure of $1 \times 10^{6}$ $P a$ . The room in which the cylinder is placed catches fire. Predict the temperature (in $K$ ) at which the cylinder will blow up before it melts (m.p.t. of the cylinder $= 1800 K)$ .

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Solution

Given, $P_{1} = 250 k P a, T_{1} = 300 K$
$P_{2} = 1 \times 10^{6} P a, T_{2} = ?$
Since, volume of cylinder remains constant
Therefore, $\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$
$\frac{250 \times 10^{3}}{300} = \frac{1 \times 10^{6}}{T_{2}}$
$T_{2} = 1200 K$
The cylinder will blow up at 1200 $K$ before melting (m.pt. 1800 $K$ ).

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An iron cylinder contains helium at a pressure of 250 kPa at 300 K. The cylinder can withstand a pressure of 1×106 Pa. The room in which the cylinder is placed catches fire. Predict the temperature (in K) at which the cylinder will blow up before it melts (m.p.t. of the cylinder =1800K).

Given, P1=250kPa,T1=300KP2=1×106Pa,T2=?Since, volume of cylinder remains constantTherefore, P1T1=P2T2250×103300=1×106T2T2=1200KThe cylinder will blow up at 1200 K before melting (m.pt. 1800 K).