Two bodies, with heat capacities c₁ and c₂ (assumed independent of temperature) and initial temperatures t₁ and t₂ respectively, are placed in thermal contact. show that their final temperature is given by t₁ = (c₁t₁ + c₂t₂)/(c₁ + c₂). if c₁ is much larger than c₂ . show that = t₁ + c₂(t₂ -t₁)/c₁.

Amichelson interferometer operating at a 600 nm wavelength has a 3.02-cm-long glass cell in one arm. to begin, the air is pumped out of the cell and mirror m2 is adjusted to produce a bright spot at the center of the interference pattern. then a valve is opened and air is slowly admitted into the cell. the index of refraction of air at 1.00 atm pressure is 1.00028.how many bright-dark-bright fringe shifts are observed as the cell fills with air?