A certain heat lamp emits 230 W of mostly IR radiation averaging 1,420 nm in wavelength. (a) What is the average photon energy in joules? J (b) How many of these photons are required to increase the temperature of a person's shoulder by 2.0°C, assuming the affected mass is 4.0 kg with a specific heat of 0.83 kcal/(kg · °C). Also assume no other significant heat transfer. (c) How long does this take (in s), assuming all radiation emitted by the heat lamp is absorbed by the person's shoulder? s †

Consider a fission nuclear explosion producing a temperature of 24 million K (25∗107 K). a) What is be the peak wavelength of the thermally produced photons? b) What is the energy (in eV) for this peak wavelength photon?

Experiments have shown that the nervous system of the human eye effectively takes about 30 "frames" per second (like a movie camera) and that when the eye is fully dark-adapted, it needs to receive only about 500 visible photons per frame from an object to register it. Out sun radiates a power of about 3.9 x 1026W at all wavelengths, peaking in the yellow region of the spectrum (but only about one-half of this energy is in the visible range). The pupil of your dark-adapted eye has a diameter of about 8 mm. Estimate how far away a star like the sum could be and still be visible to the naked eye. The nearest visible star is about 4 ly away and most stars we see in the sky are hundreds of light years away. What does this mean for most visible stars' intrinsic brightness compared to the sun's intrinsic brightness?