Question 3.7: During surgery or when a patient has suffered a cardiac arre......
During surgery or when a patient has suffered a cardiac arrest or stroke, lowering the body temperature will reduce the amount of oxygen needed by the body. Some methods used to lower body temperature include cooled saline solution, cool water blankets, or cooling caps worn on the head. How many kilojoules are lost when the body temperature of a surgery patient with a blood volume of 5500 mL is cooled from 38.5 °C to 33.2 °C? (Assume that the specific heat and density of blood are the same as for water.)
STEP 1 State the given and needed quantities.
STEP 2 Calculate the temperature change (∆T).
∆T = 38.5 °C – 33.2 °C = 5.3 °C
STEP 3 Write the heat equation and needed conversion factors.
SH_{water} = \frac{4.184 \space J}{g \space °C} 1 kJ = 1000 J
\frac{4.184 \space J}{g \space °C} and \frac{g \space °C}{4.184 \space J} \frac{1000 \space J}{1 \space kJ} and \frac{1 \space kJ}{1000 \space J}
STEP 4 Substitute in the given values and calculate the heat, making sure units cancel.
Heat \space \space \space = \space \space \space \underset{Two \space SFs}{5500 \space \cancel g} \space \space \space \times \space \space \space \underset{Two \space SFs}{5.3 \space °\cancel C} \space \space \space \times \space \space \space \frac{\overset{Four \space SFs}{4.184 \space \cancel J} }{\underset{Exact}{\cancel g \space °\cancel C} } \space \space \space \times \space \space \space\frac{\overset{Exact}{1 \space kJ} }{\underset{Exact}{1000 \space \cancel J} } \space \space = \space \space \underset{Two \space SFs}{120 \space kJ}| ANALYZE THE PROBLEM | Given | Need | Connect |
| 5500 mL of blood = 5500 g of blood, cooled from 38.5 °C to 33.2 °C |
kilojoules removed | heat equation, specific heat of water |