Question

You are swimming in the open ocean near the equator. The thermocline in this location is about \(1^{\circ} \mathrm{C}\) per 50 meters of depth. If the sea surface temperature is \(24^{\circ} \mathrm{C}\), how deep must you dive before you encounter a water temperature of \(19^{\circ} \mathrm{C} ?\)

Short answer

You must dive 250 meters deep.

Step-by-step solution

Identify the temperature difference

First, identify how much the temperature needs to change from the surface temperature to the desired temperature. We start with a surface temperature of \(24^{\circ} \mathrm{C}\) and desire a temperature of \(19^{\circ} \mathrm{C}\). Thus, the temperature difference is calculated as \(24^{\circ} \mathrm{C} - 19^{\circ} \mathrm{C} = 5^{\circ} \mathrm{C}.\)

Understand the rate of temperature change

The problem states that there is a temperature decrease of \(1^{\circ} \mathrm{C}\) for every 50 meters of depth. This means for every 50 meters you dive, the temperature decreases by \(1^{\circ} \mathrm{C}\).

Calculate how many meters correspond to the temperature change

To find out how many meters deep you need to dive to achieve a \(5^{\circ} \mathrm{C}\) decrease in temperature, use the rate of temperature change. Since the rate is \(1^{\circ} \mathrm{C}\) per 50 meters, you can set up the equation: \(5^{\circ} \mathrm{C} \times 50 \text{ meters/}^{\circ} \mathrm{C} = 250 \text{ meters}.\)

Key concepts

Temperature Gradient

In the open ocean, particularly near the equator, the concept of a temperature gradient is crucial in understanding how ocean temperatures change with depth. A temperature gradient refers to the rate at which temperature changes over a certain distance—here, specifically with ocean depth. When we are near the equator, the surface waters receive abundant sunlight, making them warmer. However, as you dive deeper into the ocean, the temperature tends to decrease due to less sunlight penetration and other factors.

In this exercise, we learned about a specific temperature gradient where every 50 meters you dive, the temperature decreases by 1°C. This is a way of quantifying how fast or slow the temperature changes as we move vertically in the water column. In the problem, starting at a surface temperature of 24°C and aiming for a cooler 19°C, we can use the given temperature gradient to calculate how deep we need to dive: 250 meters, in this case. Understanding this gradient helps in predicting at what depth certain temperature changes occur, which is vital for activities like diving or studying marine life, as different species adapt to different temperature ranges.

Oceanography

Oceanography is the study of the ocean's physical and biological properties. It encompasses everything from ocean currents to the complex chemistry of seawater and the diverse ecosystems found within it. It's a scientific discipline that combines different fields like geology, biology, and meteorology to understand the ocean in its entirety.

In this particular exercise, the idea of oceanography comes into play because we're exploring the changes in temperature with depth within the ocean. This is a tiny part of the broader study of oceanography, which looks at how these conditions affect global weather patterns, marine life distribution, and human activities. For instance, knowledge about temperature gradients informs us about the behavior of the thermocline—an important oceanic layer where temperature changes rapidly with depth. This layer can affect nutrient mixing, fish behavior, and even sonar readings used in navigation. So, this small calculation ties into understanding bigger oceanographic processes that are vital for climate studies, fisheries, and understanding the ocean's role in Earth's ecosystem.

Equatorial Waters

Equatorial waters are the areas of the ocean around the earth's equator. These regions are characterized by warm sea surface temperatures due to direct sunlight year-round. The equatorial region is known for having relatively stable temperatures at the surface but shows significant temperature change with depth, especially around the thermocline layer.

Equatorial waters typically have a pronounced thermocline because the warm surface layer sits on top of cooler, deeper layers. As a result, the temperature gradient can be quite noticeable when you dive deeper, as described in the exercise. Understanding the characteristics of equatorial waters is essential for multiple reasons, including weather prediction and marine navigation. For example, the behavior and location of marine species can vary significantly with the temperature changes in these waters, affecting fisheries and biodiversity conservation efforts.

• Warm surface temperatures are typical due to direct sunlight.
• Rapid temperature changes can occur below the surface, especially near the thermocline.
• Influences weather patterns such as tropical storms and El Niño.

This makes understanding temperature changes in equatorial waters not only a fascinating scientific pursuit but also a necessity for practical marine management.