Q1. Sunlight shining in during the daytime is absorbed by the floor, interior walls, and objects in the room, raising their temperature to 37.5°C. If the house is well insulated, you may model it as losing energy by heat steadily at the rate 6 100 W on a day in July when the average exterior temperature is 4.00°C and while the conventional heating system is not used at all. Throughout the period between 5:00 p.m. and 7:00 a.m., the temperature of the house drops and a sufficiently large "thermal mass" is necessary to keep it from dropping too far. The thermal mass can be a large quantity of stone (with specific heat 850 J/kg . °C) in the floor and the interior walls exposed to sunlight. What mass of stone is necessary if the temperature is not to drop below 18.5°C overnight?

Q2. Certain stars are thought to collapse at the end of their lives, combining their protons and electrons to form a neutron star. Such a star can be thought of as a giant atomic nucleus. If a star with a mass equal to that of the sun (of mass 1.99 × 10^30 kg) were to collapse into neutrons, what would be the radius of the star?

Respond in units of m.