Final answer:
To determine the rate of change of the difference in temperature between two spacecraft using the chain rule, we need the rates of change of both temperatures with respect to time. The chain rule would be applied to the difference in temperature as a function of both T1 and T2 temperatures.
Step-by-step explanation:
To determine the rate of change of the difference d in the temperatures the two spacecraft experience at time t=3, we apply the chain rule of calculus. If we let T1 and T2 be the temperatures of the two spacecraft, the difference in temperature is given by d = T2 - T1. To find the rate of change, we need the rates of change of T1 and T2 with respect to time.
The rate of heat transfer by conduction is given by the equation kA(T2 – T1) / d, where 'k' is the thermal conductivity, 'A' is the area through which heat is being transferred, 'T2' and 'T1' are the temperatures on the two sides, and 'd' is the thickness of the material. So, if we have the rates of change of T1 and T2 with respect to time, we can calculate the rate of change of d using the chain rule as ∂d/∂t = ∂d/∂T1 * dT1/dt + ∂d/∂T2 * dT2/dt.
It is important to note that without the actual rates of change of T1 and T2, the specific numerical answer cannot be provided. However, understanding the chain rule allows the student to set up the correct framework for finding the desired rate of change once additional information is available.