Apollo 11 what if question on survival

Factual Questions
1

Chalk this question up to too many guys, too much beer and a campfire . . .

To revise history a bit, say the Apollo LM crashed on the moon with no survivors. Michael Collins decides that he’ll stay in space with his fallen comrades, points the Command Module into outer space, fires up the engine and blasts away.

My question: How long does he survive? What kills him?

The command module supported the three astronauts for the three day trip home, which is nine man-days. So presumably there was nine days worth of water and oxygen. But was there nine days of heat? The apollo 13 guys survived the cold.

I’m guessing it was the oxygen, but how long would that hold out?

2

The Apollo capsule generated power and heat by combining oxygen and hydrogen in a fuel cell, which also generated heat and water as a result. So the limiting factor on power, heat, and breathing air all came down to how much oxygen was in the cryo tanks - when you run out of oxygen, you’re out of everything. The question then is whether your oxygen talk run out before your carbon dioxide scrubbing system becomes fully saturated. You might die of excess carbon dioxide in the cabin air before running out of oxygen and power. I don’t know which would run out first in the situation you describe.