On a hot sunny day, you get out of the swimming pool and sit in a metal chair, which is very hot. Would you predict that the specific heat of the metal is higher or lower than that of water? Explain.

The specific heat capacity of the metal is lower than that of the water as explained as follows

Explanation:

The heat capacity is a measure of propensity of a given object or matter to undergo an increase or decrease in its temperature when subject a given amount of heat, in other words, for a given mass of the substance, it is the amount of heat required to be added to cause it to have a unit temperature change

The specific heat capacity of a material or substance is the amount of heat required to be supplied to raise the temperature of a unit mass of that by one degree Celsius. It is the ratio of the heat capacity of a specimen of a substance divided by the mass of the specimen

Both the water of the swimming pool, the swimmer and the metal chair are all exposed to the same amount of heat from the sun, however the heat required to raise the water temperture by one degree Celsius is higher than heat required to raise the temperature of the metal chair by one degree hence the chairs temperature is higher than the water temperature as shown in the following equation

ΔH = m₁ * C₁ * ΔT₁ = m₂ * C₂ * ΔT₂

Where ΔH = Heat or energy supplied from the sun

m₁ = mass of water in the swimming pool

C₁ = Specific heat capacity of the water in the swimming pool

ΔT₁ = Change in temperature of the swimming pool and

m₂ = mass of metal chair

C₂ = Specific heat capacity of the metal chair material

ΔT₂ = Change in temperature of the metal chair

Where ΔH is the same for both the chair and swimming pool with the chair being hotter than the swimming pool with an asumed temperature change of 1.5 times that of the swimming pool and assuming the same mass of both the swimming pool and the chair are measured we have

m₁ * C₁ * 1.5ΔT₂ = m₁ * C₂ * ΔT₂ then cancelling like terms we have

1.5C₁ = C₂

Hence the heat capacity of the swimming pool water is 1.5 times that of the metal chair