Did Apollo 13 CM reach thermal equilibrium when it was powered down?

Question

It was reported that the CM cabin temperature dropped to 43°F. Was that the equilibrium, or would it have gotten colder if it had remained in space longer. If that wasn't equilibrium was there an estimate of the cabin temperature the CM would have been, if it had reached thermal equilibrium?

Answer 1

There were too many factors preventing the command module from reaching equilibrium. Quotes are from the mission report.

• The joined spacecraft was often in a barbecue roll.
• Although the crew spent as much time in the LM as possible, occasional excursions to the LM were needed. This including getting food, getting supplies for the improvised CO$_2$ scrubber, stowing wastes, and readying the CM for re-entry. Such activities would have disturbed any thermal equilibrium.
• Some of the output of the improvised CO$_2$ scrubber was diverted to the CM, creating some airflow.

  With ground instructions, a system was constructed which attached a command module lithium hydroxide cartridge to each of two lunar module suit hoses. The Commander's remaining hose was placed in the tunnel area to provide fresh oxygen to the command module, while the Lunar Module Pilot's remaining hose was positioned in the lunar module environmental control area.

• Considerable water condensation occurred. This would vary depending upon astronaut activity and cabin airflow.
• The drinking water tank in the CM froze up. The process of freezing releases heat, until no more liquid remains.

  The command module potable water served as the main drinking supply for the crew during the mission, and approximately 14 pounds were withdrawn after powering down, using the 8-ounce plastic bags. The crew reported at approximateliy 120 hours they were unable to withdraw water from the potable tank and assumed it was empty. Approximately 6 hours after landing, the recovery crew was also unable to obtain a water sample from either the potable or waste water tanks. The recovery personnel stated the structure near the tank and lines was very cold to touch, and an analysis of temperatures during the flight in this vicinity show that freezing in the lines most likely occurred.

• We simply don't have much data on the actual temperatures which occurred. Our knowledge is based on two brief periods of telemetry, and simulations back on the ground:

  All power to the guidance and navigation system, including the inertial measurment unit heaters, was removed at about 58 hours. Heater power was applied about 80 hours later, when the inertial measurement unit was put into standby and the computer turned on. Based upon ground test data and two short periods of telemetry, the minimum temperature is estimated to have reached 55° or 60° F before power-up.

Considering the above factors, it is unlikely that a steady-state temperature would have been reached.