Use the worked example above to help you solve this problem. A comet half a kilometer in radius consisting of ice at $273$ K hits Earth at a speed of $7\mathrm{.}10103$ m$/$s$.$ For simplicity, assume that all kinetic energy converts to thermal energy on impact and that all the thermal energy goes into warming the comet.

$($a$)$ Calculate the volume and mass of the ice.

Volume m$3$Mass kg

$($b$)$ Use the conservation of energy to find the final temperature of the comet material. Assume, contrary to fact, that the result is superheated steam and that the usual specific heats are valid, though in fact they depend on both temperature and pressure.

K

$($c$)$ Assuming the steam retains a spherical shape and has the same initial volume as the comet, calculate the pressure of the steam using the ideal gas law. This law actually doesn't apply to a system at such high pressure and temperature, but can be used to get an estimate.

Pa