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(B) The process occurs at a constant volume because the cylinder is rigid.According to Gay-Lussac's Law,for a fixed amount of gas at constant volume,t

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$1500$

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(B) The process occurs at a constant volume because the cylinder is rigid.According to Gay-Lussac's Law,for a fixed amount of gas at constant volume,the pressure is directly proportional to the absolute temperature: $P \propto T$ or $\frac{P_1}{T_1} = \frac{P_2}{T_2}$.Given:Initial pressure $P_1 = 20 \,atm$Initial temperature $T_1 = 27^{\circ} C = 27 + 273 = 300 \,K$Maximum pressure the cylinder can withstand $P_2 = 100 \,atm$We need to find the temperature $T_2$ at which the pressure reaches $100 \,atm$.Substituting the values into the formula:$\frac{20}{300} = \frac{100}{T_2}$$T_2 = \frac{100 	imes 300}{20}$$T_2 = 5 	imes 300 = 1500 \,K$Thus,the danger of explosion sets in at $1500 \,K$.

$A$ hydrogen cylinder is designed to withstand an internal pressure of $100 \,atm$. At $27^{\circ} C$,hydrogen is pumped into the cylinder which exerts a pressure of $20 \,atm$. At what temperature does the danger of explosion first set in? (in $K$)

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