You accidentally put an oil stain on your clothes and try to wash it with cold water. Why is it difficult to do?
P.S. This question was asked in class by my physics instructor, with a peculiar emphasis on cold water
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Water won't wash out an oil stain at all, whether the water is cold or hot, because oil in't soluble in water. So I assume your teacher meant washing the cloth in a surfactant (i.e. washing powder) solution of various temperatures.
In that case there are two main reasons why the cleaning decreases with reducing temperature.
Firstly the viscosity of most oils is strongly temperature dependent. As you increase the temperature the viscosity of the oil decreases and it becomes easier to physically dislodge the oil from the cloth. Since there is a limit to the amount of shear stress washing machines can generate the viscosity of the oil is an important factor.
Secondly the rate of surfactant dissolution in the oil increases with increasing temperature. This is a kinetic effect since if you wait long enough you'll get roughly the same surfactant concentrations in the oil, but most washing machines use a fixed duration washing cycle and at low temperatures this may not be long enough to get surfactant thoroughly dissolved into the oil.