I’m carrying difficulty removing this problem:
Microwaves prepare by emitting deviation with a magnitude of 2.45x109s-1. Calculate a series of photons compulsory to lift 274.0 g H2O from twenty-nine C to 100 C, a hot point. Assume a feverishness genius of H2O is consistent over this heat operation as well as is next to to 4.2 J/g-K.
Thank you
It’s been a while since I did physics, so bear with me here…
Firstly, you will want to know how much energy the water is going to require to raise it from 29 to 100 deg C. Simple – we use
Q = mC(T2 – T1)
= 274.0 g x 4.2 J/g.K x (100 – 29)
= 81.7 kJ.
Keep in mind that we aren’t considering a phase change here – if we were, we would have to add in enthalpy of vapourization to the total energy.
I forget the name of the equation, but the relationship between the energy of a photon and its wavelength is given by
E = hc/lambda
Where E is energy, h is plank’s constant, c is the speed of light in m/s, and lambda is the wavelength of the photon.
But we don’t know it’s wavelength, we know its frequency! Luckily, there is yet another equation which relates velocity to wavelength and frequency of a wave, and that is:
lambda = v/f
Where lambda = wavelength, v = velocity, and f = frequency.
Plugging in 3 x 10^8 m/s (speed of light) and 2.45 x 10^9 s^-1, I get a wavelength of 0.122 m.
Plugging that into E = hc/lambda, I get an energy of 1.63 x 10^-24 J/photon.
All I need to do now is divide my required energy to heat my water by the number of joules per photon, and I’ll get number of photons, which happens to be around 5.01 x 10^28 photons! Done!
Energy used E= m*c*(tf-ti)
E= 274*4.2*(100-29)=81707 J
Energy of one photon E=h*f = 6.63*10^-34*2.45*10^9=1.624*10^-24J=5.03*10^28 photons