An iron cylinder contains helium at a pressure of 250 k Pa at 300 K. The cylinder can withstand a pressure of `1 xx 10^6` Pa. The room in which cylinder is placed catches fire. Predict the temperature (in K) at which the cylinder will blow up before it melts or not (m.p.t. of the cylinder =1800K)..

Explanation

Since the gas is confined in the cylinder, its volume will remain constant, i.e. `V_(1) = V_(2)` at every temperature till the gas remains in cylinder.  Initial conditions `P_(1) = 250 Pa = 250 × 10^(3) Pa`
`T_(1)=300K`
Final conditions `P_(2) = ?`
`T_(2) = 1800 K`
by applying gay lussac’s law, `(P_(1))/(T_(1))=(P_(2))/(T_(2)) implies (250xx10^(3))/(300)=(P_(2))/(1800)`
`P_(2)= (1800xx250xx10^(3))/(300)= 1.5xx10^(6) Pa`
`"Pressure at melting point of the cylinder" = 1.5 xx 10^(6)`
But since the cylinder can withstand a pressure of `1 xx 10^(6) Pa`, it will definitely blow up at the m.p. of the cylinder when the pressure become `1.5 xx 10^(6) Pa`