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#+TITLE: Cooking Thermodynamics

How much time does it take to boil water in room temperature?

* Analysis 

** Energy Balance

The change in internal energy is equal to the energy absorbed by the food 

\[ \Delta U = Q \ m \bar{c_p} \Delta T = \bar{\dot{Q}} \Delta t \]
 
** Assumptions for boiling water

Water temperature increases from 5$ to 00^\circ\text{C}$

\[\Delta T=75^\circ\text{C}\]

\[ \bar{c_p}= 4.2 \text{ kJ/kg-K}\]

** Heater temperature

Heaters are about 000 \text{ W}$. Let's say 0\%$ gets lost to the environment

\[ \bar{\dot{Q}} = 1.8 \text{ kW} \]


** Result

Substituting in the energy balance equation above, and making the time in minutes

\[ m \text{ [kg]} (4.2)(75) = (1.8) \Delta t \text{[min]} (60) \]

\[ \Delta t \text{[min]}  \approx 3 m\text{ [kg]} \]