Ch. 20 - Second Law of Thermodynamics

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 20 - Second Law of Thermodynamics

Problem 80

Chapter 20, Problem 80

Two 1100-kg cars are traveling 75 km/h in opposite directions when they collide and are brought to rest. Estimate the change in entropy of the universe as a result of this collision. Assume T = 20°C.

Verified step by step guidance

Convert the speed of the cars from km/h to m/s using the conversion factor: 1 km/h = 1000 m / 3600 s. This will give the velocity in SI units.

Calculate the initial kinetic energy of each car using the formula for kinetic energy:

K_{i} = (1/2)mv²

, where

m

is the mass of the car and

v

is its velocity. Since both cars have the same mass and speed, calculate the total initial kinetic energy by summing the kinetic energy of both cars.

After the collision, the cars come to rest, so their final kinetic energy is zero. The change in kinetic energy is equal to the total initial kinetic energy, which is converted into heat energy during the collision.

Estimate the change in entropy of the universe using the formula:

Δ S = \frac{Q}{T}

, where

Q

is the heat energy (equal to the change in kinetic energy) and

T

is the temperature in Kelvin. Convert the given temperature from Celsius to Kelvin using the formula:

T

_k = T_c + 273.15.

Substitute the values for

Q

(total initial kinetic energy) and

T

(temperature in Kelvin) into the entropy formula to calculate the change in entropy of the universe.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Conservation of Momentum

In a collision, the total momentum of a closed system remains constant if no external forces act on it. For two cars colliding, their momenta before the collision must equal their momenta after the collision. Since both cars come to rest, the momentum change can be analyzed to understand the forces involved during the impact.

Kinetic Energy and Work-Energy Principle

Kinetic energy is the energy an object possesses due to its motion, calculated as 1/2 mv². In a collision, this kinetic energy is transformed into other forms of energy, such as heat and sound, leading to a loss of mechanical energy. Understanding this transformation is crucial for estimating the energy dissipated during the collision.

Entropy and the Second Law of Thermodynamics

Entropy is a measure of disorder or randomness in a system, and the Second Law of Thermodynamics states that the total entropy of an isolated system can never decrease over time. In the context of the collision, the energy dissipated as heat increases the entropy of the universe, reflecting the irreversible nature of the collision process.

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