Problem 72 - Pearson Physics

Question

Predict \& Explain (a) If you rub your hands together, does the entropy of the universe increase, decrease, or stay the same? (b) Choose the best explanation from among the following: A. Rubbing the hands together draws heat from the surroundings and therefore lowers the entropy. B. No mechanical work is done by the rubbing and hence the entropy does not change. C. The heat produced by the rubbing raises the temperature of the hands and the air, which increases the entropy.

Step-by-Step Solution

Answer

(a) Entropy of the universe increases. (b) Explanation C is correct.

Step 1: Understand Entropy

Entropy is a measure of disorder or randomness in a system. When energy is spread out or dispersed, entropy increases. According to the second law of thermodynamics, the total entropy of an isolated system can never decrease over time.

Step 2: Define the Process

When you rub your hands together, mechanical work is converted into heat due to friction. This heat raises the temperature of your hands, which means energy is being dispersed into your hands and the surrounding air.

Step 3: Analyze Entropy Change

Since the action of rubbing your hands creates heat through friction, this heat increases the temperature of both your hands and the surrounding air, leading to more molecular movement and disorder. Hence, the entropy of the system (your hands and the surrounding air) increases.

Step 4: Select the Best Explanation

Among the options, only C correctly explains what happens: 'The heat produced by the rubbing raises the temperature of the hands and the air, which increases the entropy.' This aligns with the idea that increased molecular motion raises entropy.

Key Concepts

Entropy

Entropy is a key concept in thermodynamics related to disorder or randomness. It helps us understand how energy is spread out within a system. Imagine a neatly stacked pile of books. If these books were suddenly scattered all over, they would represent a higher entropy state. Similarly, in physical systems, when energy such as heat is dispersed more widely, entropy increases.

• More disorder means higher entropy.
• Energy dispersal leads to increase in entropy.

In our exercise, when you rub your hands together, they become warmer. This is because mechanical energy (the act of rubbing) gets converted into heat energy, increasing the disorder as it spreads into your hands and the air, thereby raising entropy.

Second Law of Thermodynamics

The second law of thermodynamics tells us that the entropy of an isolated system can never decrease; it either stays the same or increases. This law is a fundamental principle that explains the natural tendency of systems to move towards more disorder.

• Entropy tends to increase in isolated systems.
• Energy transformations are rarely efficient, often leading to increased entropy.

In the context of rubbing hands, we are not talking about an isolated system, since the surroundings are involved. However, the heat generated increases entropy locally. This illustrates that mechanical work often results in entropy increase due to energy dispersal.

Heat Transfer

Heat transfer is an essential concept in understanding thermodynamics. It describes how thermal energy moves from one body to another, typically from a warmer object to a cooler one. This is why, when you rub your hands, they feel warm – heat is transferred due to friction.

• Heat flow is from high to low temperatures.
• Friction is a common way where mechanical actions convert into heat energy.

The heat generated by rubbing spreads through your skin and into the surrounding air, raising temperatures and increasing entropy. Such processes exemplify how energy is transferred and leads to changes in entropy in a system.

Friction

Friction is the force that opposes motion when two surfaces are in contact. It’s the key reason why your hands warm up when you rub them together. Though it often makes systems less efficient by converting some kinetic energy into heat, this heat can be useful at times.

• Friction turns motion into heat energy.
• It plays a critical role in everyday processes.

In the exercise, when you rub your hands, friction generates heat. This heat contributes to raising the temperature and increasing entropy, as energy is transferred from movement to thermal energy. Friction is a natural way through which energy dispersal occurs in many activities.