The refining method used when the metal and the impurities have low and high melting temperatures, respectively, is liquefaction.

Explanation:
When a metal is extracted from its ore, it often contains impurities that need to be removed in order to obtain a pure metal. One common method of refining metals is by using the difference in melting temperatures between the metal and the impurities.

Liquefaction:
Liquefaction is a refining method that takes advantage of the different melting temperatures of the metal and the impurities. In this process, the impure metal is heated to a temperature where it melts, while the impurities remain solid. This allows the impurities to be separated from the molten metal, resulting in a purer product.

Advantages of Liquefaction:
Liquefaction has several advantages as a refining method:
1. High purity: Liquefaction can produce a very high purity metal since the impurities are separated from the molten metal.
2. Selective removal: Liquefaction allows for the selective removal of impurities based on their different melting temperatures.
3. Efficient: Liquefaction is an efficient method of refining because it takes advantage of the physical properties of the metal and the impurities.

Other Refining Methods:
While liquefaction is suitable for metals and impurities with different melting temperatures, there are other refining methods used for different scenarios:
1. Zone refining: Zone refining is used when impurities are evenly distributed throughout the metal. It involves passing a molten zone through the metal, causing the impurities to move along with it.
2. Vapour phase refining: Vapour phase refining is used when the metal can form volatile compounds with impurities. The impurities are converted into volatile compounds, which are then removed through vaporization.
3. Distillation: Distillation is used when the metal has a much lower boiling point than the impurities. The metal is vaporized and condensed, while the impurities remain behind.

In conclusion, liquefaction is a refining method used when the metal and the impurities have low and high melting temperatures, respectively. It is an efficient and selective method that allows for the production of high purity metals.