All mixed up!

A can of volume \(1\text{ m}^3\) is filled with a hypothetical gas at \(300 \text{ K}\) and initial pressure \(1.0 \times 10^6 \text{ Pa}\). The mass of can is \(6 \text{ kg}\). The can is now kept in a incinerator and heat is supplied to it power \(1000t \text{ W/s}\) where \(t\) is in seconds. The 'can' can withstand a maximum pressure of \(8.0 \times 10^6 \text{ Pa}\). The specific heat of can is \(500 \text{ J/(kg.K)}\) and that of gas is \(900 \text{ J/(kg.K)}\). The coefficient of volumetric expansion of can is \(2 \times 10^{-5} \text{ K}^{-1}\).

Find the time (in seconds to the nearest integer) after which the can will explode. Take molar mass of gas same as that of hydrogen gas and \(R=25/3 \text{ Pa m}^3 \text{/(mol K)}\).

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