# Why is water used for cooking

## Internal energy - heat capacity

a) The temperature rises within the first 5 minutes from \ (20 \, {} ^ {\ circ} \ rm {C} \) to \ (100 \, {} ^ {\ circ} \ rm {C} \) almost evenly. After that it remains largely constant at around \ (100 \, {} ^ {\ circ} \ rm {C} \).

b) In the first five minutes, the energy supplied by the gas flame is used to heat the water and the potatoes, then to evaporate the water. During the whole time, part of the supplied energy is released into the environment.

c) After five minutes, only the energy that is given off to the environment or escapes with the water vapor needs to be supplied. The gas flame can be adjusted accordingly. If too much gas is burned in this phase, unnecessarily much water evaporates and thus more water vapor escapes.

d) If one needs \ (4 {,} 19 \, \ rm {kJ} \) energy to \ (1 \, \ rm {kg} \) water by \ (1 \, {} ^ {\ circ} \ rm {C} \), one needs to heat \ (1 {,} 5 \, \ rm {kg} \) water by \ (100 \, {} ^ {\ circ} \ rm {C } -20 \, {} ^ {\ circ} \ rm {C} = 80 \, {} ^ {\ circ} \ rm {C} \): \ [4 {,} 19 \ cdot 1 {,} 5 \ cdot 80 \, \ rm {kJ} = 5 {,} 0 \ cdot 10 ^ 2 \, \ rm {kJ} \] You need an energy of approx. 500 kJ in the first five minutes.

e) The chemical energy in \ (0 {,} 054 \, \ rm {m} ^ 3 \) natural gas is \ [0 {,} 054 \ cdot 39 \ cdot 10 ^ 3 \, \ rm {kJ} = 21 \ cdot 10 ^ 2 \, \ rm {kJ} \] In the first five minutes, approx. 2100 kJ of energy were released into the saucepan and the surrounding area when it was burned. Approx. 500 kJ were used to heat the water and the potatoes.

The following applies to the efficiency

\ [\ eta = \ frac {{\ Delta {E _ {\ rm {i}}}}} {{\ Delta {E _ {{\ rm {chem}}}}}} \ Rightarrow \ eta = \ frac {{ 5 {,} 0 \ cdot {{10} ^ 2} \, {\ rm {kJ}}}} {{21 \ cdot {{10} ^ 2} \ cdot {{10} ^ 2}}} = 0 {,} 24 = 24 \% \] The efficiency results in a value of 24%.

f) Because of the smaller amount of water, less energy is required. Water vapor, which has a temperature of approx. 100 ° C, forms above the surface of the water. This water vapor promotes the cooking of the potatoes as does the boiling water.

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