Specific heat of a substance can be defined as the amount of heat required to raise its temperature by 1 degree Celsius. Water has a very high specific heat, among the common substances. The specific heat of water is 4.186 J/gm per degree Celsius, that is , it requires 4.186 J of energy to heat 1 gm of water and increase its temperature by 1 degree Celsius. Among fluids, ammonia has the highest specific heat at 6.74 J/gm per degree Celsius (at 238 Fahrenheit). Rocks have relatively lower specific heats and only magnetite, kyanite and hematite have similar specific heat values.
For a substance to have infinite specific heat value, it would have to be a perfect sink. Only then will the substance consume an infinite amount of energy without any increase in temperature. Thus, it will act as a perfect isothermal system. Such a perfect sink is not yet known to us. All the substances that we know have a finite specific heat (check the links for specific heat values for rocks and fluids).
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