The graph of the heating of methanol has been attached.
The temperature at 170 K is approximately the melting point of methanol.
The temperature at 350 K is approximately the boiling point of methanol.
If we provide heat before 170 K temperature then all the heat provided to the methanol will result in rise in temperature of methanol in solid form.
If we provide heat at 170 K temperature then all the heat provided to the methanol will result in change in physical from of methanol from solid to liquid.
If we provide heat after 170 K temperature and before 350 K temperature then all the heat provided to the methanol will result in rise in temperature of methanol in liquid form.
If we provide heat at 340 K temperature then all the heat provided to the methanol will result in change in physical from of methanol from liquid to gas.
If we provide heat after 350 K temperature then all the heat provided to the methanol will result in rise in temperature of methanol in gas form.
So, the heat given to methanol will rise its temperature except at its Boiling and melting point. At those temperature heat will change the physical form of methanol first. and the graph also have been attached of between boiling point and melting point as given in question .
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