Question

The specific heat capacity of platinum is 0.032 cal/g·K. How to calculate the heat, in joules, necessary to raise the temperature of a sample of platinum weighing 20.0 g from 15.0 Celsius to 65.0 Celsius?

Answer 1

You have to convert either the specific heat of platinum, or the actual heat required from Cal/g K to J/g K. I"ll convert the specific heat and calculate the heat directly in Joules.

So, in order to get from calories per g Kelvin to Joules per g Kelvin you must use a conversion factor

`0.032"cal"/("g" * "K") * "4.184 J"/"1 calorie" = 0.134"J"/("g" * "K")`

The relationship between heat and temperature change is expressed mathematically through this equation

`q = m * c * DeltaT`, where

`q` - the heat supplied;
`m` - the mass of the sample;
`c` - the specific heat of, in your case, platinum;
`DeltaT` - the change in temperature;

Solving for `q` will get you

`q = "20.0 g" * 0.134"J"/("g" * "K") * (338.15 - 288.15)"K" = "+134 J"`

Notice how little energy is needed to raise the temperature of a `"20.0-g"` sample of platinum by 50 degrees; by comparison, you would need approximately 30 times more energy to raise the temperature of this much water by 50 degrees.