Dry methane is supplied by a compressor and pre cooling system to the cooler of a Linde liquid methane system. At 180 bar and 300 K. The low–pressure methane leaves the cooler at a temperature 6 C lower than the temperature of the incoming high pressure methane. The separator operates at 1 bar, and the product is saturated liquid at this pressure. What is the maximum fraction of the methane entering the cooler that can be liquefied?