Object P (a metal sphere) is initially at 90 °C, and object Q (an identical metal sphere) is initially at 30 °C. The two spheres are placed in thermal contact inside an insulated chamber. After 10 min they are separated, at which point both spheres are at 60 °C. Without delaying, sphere Q is placed in thermal contact with a third identical sphere R that is initially at 20 °C and is also inside an insulated chamber. After an additional 10 min, spheres Q and R are separated at a common temperature of 45 °C.
Assume no energy is exchanged with the surroundings during either 10-min interval.
(a) Sketch a qualitative graph of the temperature of sphere Q as a function of time over the entire 20 min experiment. Clearly label the key temperature values and the times at which the spheres are brought into and removed from contact.
(b) Explain the shape of your graph in part (a) by discussing the direction of energy transfer during each 10-min interval and citing the definition of thermal equilibrium.
(c) Immediately after the second 10-min interval ends, spheres P and R are at 60 °C and 45 °C, respectively. Predict the initial direction of net energy transfer if these two spheres are placed in thermal contact, and justify your prediction without performing numerical calculations.