## Saturday, February 25, 2006

### Calculate the Thermal Capacity of a Fluid

a) What is the Thermal Capacity of a liquid, given the following details:

Volume = 200ml

Specific Gravity = 0.8

Specific Heat = 1.5 cal/g/degC

b) Also, assuming there are no external heat losses, calculate the energy required to raise the sample's temperature to 37 degC.

a) The Thermal Capacity of a sample is the amount of heat energy required to raise the specific sample by one degree celcius. This can calculate from the given data as follows:

Weight of Sample = Specific Gravity * Weight of Same Volume of Water

Weight of Sample = 0.8 * 200 g

Weight of Sample = 160g

Water has a density of one gram per milliliter.

Then:

Thermal Capacity = Weight of Sample * Specific Heat

Thermal Capacity = 1.5 cal/g/degC * 160g

Thermal Capacity = 240 cal/degC

It is reassuring to see that the final result has the correct units to be a thermal capacity - an amount of energy per unit of temperature!

b) The thermal capacity we just calculated is the energy required to raise this samples temperature by one degree celcius. Now, we want to go from 22 to 37 degC, so we need to multiply the thermal capacity by 15 degC to get the number of calories required.

Energy = Thermal Capacity * Temperature Change

Energy = 240 cal/degC * 15 degC

Energy = 3600 cal

/ul] Again, we are reassured by the fact that the units work out correctly.

In fact, it should be noted that this entire problem can be done with very little physics knowledge - pure application of dimensional analysis to the quantities given and wanted (and their units) can quickly solve this problem!