Problem 66 - College Physics

Question

Human adult blood contains, on average, \(7000 / \mathrm{mm}^{3}\) white blood cells (leukocytes) and \(250000 / \mathrm{mm}^{3}\) platelets (thrombocytes). If a person has a blood volume of \(5.0 \mathrm{~L}\), estimate the total number of white cells and platelets in the blood.

Step-by-Step Solution

Answer

There are 35 billion white blood cells and 1.25 trillion platelets in 5 liters of blood.

Step 1: Convert Blood Volume to Cubic Millimeters

Since the given values for blood components are per cubic millimeter, we first need to convert the blood volume from liters to cubic millimeters. Knowing that 1 liter equals 1,000,000 cubic millimeters, the 5.0 liters of blood is equivalent to \(5.0 \times 1,000,000 = 5,000,000\) cubic millimeters.

Step 2: Calculate Total Number of White Blood Cells

The average concentration of white blood cells is 7000 per \(\text{mm}^3\). To find the total number of white blood cells, multiply the concentration by the total blood volume in \(\text{mm}^3\). This gives \(7000 \times 5,000,000 = 35,000,000,000\) white blood cells.

Step 3: Calculate Total Number of Platelets

The average concentration of platelets is 250,000 per \(\text{mm}^3\). To find the total number of platelets, multiply the concentration by the total blood volume in \(\text{mm}^3\). This gives \(250,000 \times 5,000,000 = 1,250,000,000,000\) platelets.

Key Concepts

White Blood Cells

White blood cells, or leukocytes, are an essential component of the human immune system. These cells play a crucial role in defending the body against infections and foreign invaders. There are several types of white blood cells, each with its specific function. For example, neutrophils quickly respond to bacterial infections. Lymphocytes, on the other hand, are crucial in identifying and neutralizing viruses.
White blood cells are found throughout the body, including the blood and lymphatic system. They constantly circulate and patrol the body, ready to spring into action when a threat is detected.
On average, adult human blood contains about 7000 white blood cells per cubic millimeter. This number can vary depending on various factors such as age, health status, and current infections. A blood cell count provides critical insight into a person's immune health. A significant increase or decrease could indicate underlying medical conditions.

Platelets

Platelets, also known as thrombocytes, are tiny blood cells instrumental in the blood clotting process. When a blood vessel is damaged, platelets clump together at the site to form a clot, helping to stop bleeding. This is a vital mechanism for preventing excessive blood loss.
With an average concentration of 250,000 platelets per cubic millimeter of blood, these cells play a major role in maintaining the circulatory system's integrity. Unlike other blood cells, platelets are relatively small and do not carry oxygen.
Platelets are produced in the bone marrow and have a lifespan of about 8-10 days. Monitoring platelet count can help diagnose and evaluate conditions like thrombocytopenia, where platelet levels are too low, or thrombocytosis, where they are abnormally high.

Biological Quantities

In biology, quantities such as the count of cells or concentration of molecules are fundamental. They offer a quantifiable measure to understand biological processes.
These quantities are crucial in research and clinical diagnostics. For instance, knowing the typical range of white blood cells guides doctors in diagnosing immune disorders. Similarly, platelet count is vital in assessing blood clotting readiness.
Biological quantities are typically expressed in terms per unit volume or mass, such as cells per cubic millimeter. This standardization helps in comparing results across different studies and populations. Understanding and interpreting these quantities is essential for progressing in fields like medicine, biochemistry, and genetics.

Unit Conversion

Unit conversion is an essential skill in scientific calculations, allowing us to work with values in different measurement systems. In the context of blood cell count, we often need to convert units such as liters to cubic millimeters to match the units used in biological measurements.
For example, when dealing with blood volume, you might start with liters but need to convert to cubic millimeters because cell concentrations are frequently given per cubic millimeter. Remembering that 1 liter is equivalent to 1,000,000 cubic millimeters is very useful.
This conversion ensures accuracy in calculations and comparisons. Incorrect unit conversions can lead to significant errors in scientific conclusions. Practicing unit conversion helps build precision and confidence in tackling scientific problems efficiently.