Question

Starting from the lower triple point what actions) would produce liquid carbon

Answer 1

Liquid carbon dioxide forms only at pressures above 5.1 atm; the triple point of carbon dioxide is about 518 kPa at 56.6 C. At this temperature and pressure CO2 will exist as a solid, liquid and gas. You cannot get a liquid by cooling alone - you have to increase the pressure as shown.

Answer 2

The phase diagram required to answer this question is missing but I have attached the image to this answer.

The lower triple point is the point of the diagram where all three phases meet, roughly around 4000 K. In order to produce liquid carbon, we must change either the temperature and/or pressure to cause this change in state. If we were to simply raise the temperature, we would move to the right of the triple point which would enter the gaseous phase. If we only changed the pressure, we we would move up from the triple point, which would still be solid phase. Therefore, we must raise BOTH the temperature and the pressure to reach the liquid phase for carbon.