In terms of heat capacity, explain why a lake will be cold on a spring day when the air temperature is warm and why the water in a lake be warm on a cool fall day?
Heat capacity can be defined as the amount of heat needed by the system to change the temperature of a given amount of system. The temperature of the water in a lake or other water system tends to have a similar temperature all throughout. Water is able to equilibrate its temperature with the soils temperature thus keeping its temperature in the same degrees. Heat capacity allows the water in the lake to have the same temperature with the soil.
What really differs is the temperature of the air which apparently affects the human sensory system.
During warm season, the external temperature is higher so our body tends to equilibrate with that temperature. Since we are now familiar with the current temperature, we will sense that the temperature of the water in the lake to be colder. On the other hand, when the external temperature is colder during winter, the temperature of water still hasn't changed that much. Our body respond to the cold weather thus making our sensory organ give the sense of hot to the body when we tough the water.