# 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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