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# Microwave ovens use microwave radiation to heat food. The

ISBN: 9780321696724 27

## Solution for problem 97IE Chapter 6

Chemistry: The Central Science | 12th Edition

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Chemistry: The Central Science | 12th Edition

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Problem 97IE

Problem 97IE

Microwave ovens use microwave radiation to heat food. The energy of the microwaves is absorbed by water molecules in food and then transferred to other components of the food. (a) Suppose that the microwave radiation has a wavelength of 11.2 cm. How many photons are required to heat 200 mL of coffee from 23 to 60 °C? (b) Suppose the microwave’s power is 900 W (1 watt = 1 joule-second). How long would you have to heat the coffee in part (a)?

Step-by-Step Solution:
Step 1 of 3

1,2 ,…, 1,2,…, 1,2,…, 12 1 4 [2 11 4] 1 3 7 = 5,10,15 )⃗ 1 7 1 4 1 0 1 ⃗ 2 6 4 ] [0 1 ] 1 3 2 2 0 0 0 1 − 2  ⃗⃗⃗ [ 1] 3 − 2 1 1 − 1 = 5 [− ] 2 1 3 2 [2] = 10 2 ] = 15 1 1 10 0 0 0 1 0 0 −2 0 0 −5 0 0 [0 −4 0] [ 0 4] [0 0 −7 0 ] 0 0 5 0 0 0 6 1 0 0 [ 0 0 ] 2 0 0 3 −2 0 (−2) 0 [ 0 4] [ 0 4] 7 2 [−4 1 ] 1 1 5 0 [−1 −2 ] [0 3 ] [2 1 ] −1 −1 1 1 5 0 2 1 [−1 −2][ 0 3][−1 −1 ] 2.5 − 3 5 − 3 [2.3 − 2.5 2.3 − 5] × 0 −1 −1 [ 1 2 1] = 0 = 1 −1 −1 0   0 −1 −1 [ 1 2 1] −1 −1 0 1 0 −1 [0 1 1] 1 0 0 0  {[−1]} 1  −1 −1 −1 [ ] 1 1 1 −1 −1 −1 −1 −1 −1 [ 0 0 0 ] 0 0 0 −1 −1  {[ 1],[ 0]} 0 1  = 1 1 −1 −1 [−1],[1 ] [ 0] 1 0 1 ≤ dim( ) ≤ 1,2,…, ,,…, 0 0 1 [0 2 0 ] [,, 0 0 3 0 0 3 [0 1 0 ] ,,] 0 0 2 1= 0, 2 1, 3 1 0 0 [0 0] 0 0 1 −1 −1 1 [−1 ] 2 [ 1 ] 3 [ 0] 1 0 1 2 3 1 −1 −1 [−1 1 0 ] 1 0 1 1 1 1 [ 1 2 1] −1 −1 0 1 −1 −1 0 0 0 1 1 1 [−1 1 0 ][0 1 0 ][1 2 1] 1 0 1 0 0 1 −1 −1 0

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Microwave ovens use microwave radiation to heat food. The