Specific Heat

In the case of blood and water, the two fluids have different capacities for holding heat. Thus, the temperature of the mixture has to be calculated slightly differently. The general equations for mixing two fluids, in particular room temperature water and ice water, are explored here.

Heat is measured in a quantity called calories. The amount of heat an object has certainly depends upon the temperature of the object and the size of the object. For example, it takes more energy to heat a large pan of water than a small pan. Objects 'hold' heat differently. Thus, another important quantity is the amount of heat an object can hold per unit volume at different temperatures. This quantity is called the specific heat capacity of the object.

The amount of heat in a volume of fluid v (ml or cc) with temperature T (° C) and specific heat capacity of C (cal per cc per °C) is given by the equation:

Amount of Heat = v x T x C

So the amount of heat in a mixture of room temperature water and ice water can be calculated by:

Total Amount of Heat = v_w x T_w x C_w + v_i x T_i x C_i

and the temperature of the mixture can be found using:

where v_w is the volume of water, T_w is the temperature of the water, C_w is the specific heat of water, and v_i, T_i, and C_i are the corresponding elements for the injectate (ice water). The problem with this equation is that we don't know the volume of water that the ice water is mixing since this depends upon the flow rate. However, all that we need is the concentration of ice water. In the case of water and ice water, the specific heats are the same and can be assumed to be 1. Thus the temperature of the mixture is:

Recall that the concentration can be calculated using the expression:

Combine these two results to show that:

Similar calculations can be done in the case of blood and ice water where the specific heat capacities are different.