The Math of "The Martian" Sol 68

Not using the heater didn’t work out. The Rover doesn’t have enough insulation to keep the body heat that Mark generates from leaking out of the Rover. 

Mark’s new plan is to dig up the Radioisotope Thermoelectric Generator (RTG) that powered the MAV fuel plants until the crew arrived and connected the MAV to power form the solar panels.

The RTG turns heat form naturally radioactive Plutonium-238 into electricity. The RTG has two layers of shielding to protect the crew from the radiation produced, as long as both don’t crack it is safe. None the less, once the MAV was connected to the solar panels the crew took the RTG 4 kilometers away from the Hab and buried it.

It’s also not that efficient, the Plutonium inside generates 1500 Watts of heat, but it is only able to convert that into 100 Watts of electricity. But Mark wants it for the heat anyways.

How long would it take to heat 5000 Liters of air, the approximate volume inside the Rover, from -55C, the overnight low on Equatorial Mars, to 20C, a comfortable temperature?

To control the temperature Mark cut large portion of the Rover’s insulation off the wall. He can remove it when the Rover gets too hot, which will allow the heat to escape faster than the RTG can generate it. He can put it back up when it gets to cold, which will allow the RTG to generate heat faster than it leaks out.