Microwave ovens have become popular in kitchens everywhere. they are also used in the laboratory, particularly in drying samples for chemical analysis. a typical microwave oven uses radiation with a 12.2 cm wavelength. a.how many moles of photons of this radiation are required to raise the temperature of 345 g of water from 26.5 ºc to 99.8 ºc? b. the watt is a unit of power—the rate at which energy is delivered or consumed: 1 w = 1 j/s. assume that all the energy of a 700. w microwave oven is delivered to the heating of water described in (a). how long will it take to heat the water?

(a)

First of all, we need to calculate the energy needed for to raise the temperature of the water:

where

m = 345 g is the mass of the water

Cs = 4.186 g/J C is the specific heat of water

is the change in temperature of the water

Substituting,

Then we can calculate the energy of one microwave photon with wavelength

:

where h is the Planck constant and c is the speed of light

So the total number of photons needed is

And the corresponding number of moles is

where is the Avogadro number (the number of photons in 1 mole).

(b) 151.4 s

The power delivered by the microwave oven is

P = 700 W

We know that the power is the ratio of the energy delivered by the time taken:

since in this case the total energy needed to heat the water is , then the time needed is

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.