A nuclear device is tested underground in a 30-meter-diameter spherical cavern. In an instant, the fireball fills the cavern at a temperature of 10,000 K. Light from the cavern is brought to instruments through a 1,000-meter-long, 100-cm-diameter duct. a. Worst case, at what rate (KW) does heat reach the instrument? b. If the duct length is doubled, will the radiation heat rate be affected, yes or no? Why? c. A guillotine mechanism cuts the duct and blocks the light 100 milliseconds after device detonation. How much energy (J) will the instruments absorb during the test?