# To discover warm water

Chemistry Level pending

You have a plastic cup that is filled with 100 $$\mbox{g}$$ of water at 99 $$\mbox{deg C}$$. A pot of water is brought to boil (with $$V_{\mbox{pot}} \gg V_{\mbox{cup}}$$) after which the cup is suspended in the boiling water. About how long does it take for the water inside the cup to begin to boil?

Assumptions

• the cup does not touch the pot itself.
• the rim of the cup does not go under the surface of the water.
• the water in the plastic cup is below the water level in the pot.
• the specific heat of water is 4.186 $$\mbox{J} \mbox{ g}^{-1}\mbox{ deg C}^{-1}$$.
• the cup has thermal conductivity $$\gamma_H = 0.23 \mbox{ W m}^{-1}\mbox{deg K}^{-1}$$.
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