Chapter 16: Problem 71

A friend who's skeptical about climate change argues that the roughly \(0.75^{\circ} \mathrm{C}\) increase in Earth's temperature during the industrial era could be caused by an increase in the Sun's power output. The Sun's average power has, in fact, increased by about \(0.04 \%\) during this time. Could your friend be right?

Short Answer

Expert verified

The actual calculations need to be performed to verify the estimated temperature change. However, a rough calculation shows that the increase in temperature due to the increase in solar power is likely to be small, falling significantly short of the observed 0.75°C increase. Thus, it's unlikely that the 0.04% increase in the Sun's power output during the industrial era could solely cause the 0.75°C increase in Earth's temperature.

Step by step solution

Compute the Initial Solar Power Received by Earth.

Calculate the initial power received by the Earth using the Stefan-Boltzmann law, which states the power radiated per unit area of a blackbody is directly proportional to the fourth power of its temperature. Here, use the average solar constant for Earth, \(1361 W/m^2\). The total power, \(P_{sun}\), received by Earth from the Sun is therefore given by:\[P_{sun} = 1361 W/m² * 4πr²\]where \(r\) is the Earth’s radius, \(6.371e6\) m.

Compute the Increased Power Received

Since the Sun's power output increased by 0.04%, we need to compute the increased power received:\[P_{increase} = 0.0004 * P_{sun}\]

Determine the Hypothetical Change in Temperature

Next, use the Stefan-Boltzmann law to find how this power increase could theoretically affect Earth's temperature. The law states that:\[P_{increase} = σ * A * ΔT^4\]where \(σ\) is the Stefan Boltzmann constant (\(5.67e−8 W/m²K^4\)), \(A\) is Earth's surface area (\(4πr^2\)), and \(ΔT\) is the change in temperature. Solving for \(ΔT\), you find how much temperature would increase by theoretically if all the increased solar power went into heating Earth.

Compare with Actual Temperature Increase

Finally, compare the predicted temperature increase from step 3 with the actual increase of 0.75°C. If they match closely, it would suggest the friend might be correct. If they do not match closely, it would suggest that the Sun's power output is not the primary cause for Earth's temperature increase during the industrial era.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Compute the Initial Solar Power Received by Earth.

Compute the Increased Power Received

Determine the Hypothetical Change in Temperature

Compare with Actual Temperature Increase

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Measurements

Astrophysics

Force

Dynamics

Electricity

Fields in Physics

Study anywhere. Anytime. Across all devices.