On a hot summer day, 4.00 ×10^6 J of heat transfer into a parked car takes place, increasing its

step 1 Problem 48, Chapter 15, and we are asked, what is the increase in entropy of the car due to the

On a hot summer day, 4.00 ×10^6 J of heat transfer into a...

On a hot summer day, $4.00 \times 10^{6} \mathrm{J}$ of heat transfer into a parked car takes place, increasing its temperature from $35.0^{\circ} \mathrm{C}$ to $45.0^{\circ} \mathrm{C} .$ What is the increase in entropy of the car due to this heat transfer alone?

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Key Concepts

Clausius Definition of Entropy Change

According to Clausius, the change in entropy for a reversible process can be calculated by integrating the heat transfer divided by the temperature at which the transfer occurs, expressed as ?S = ?(?Q_rev/T). This relationship connects heat transfer and temperature changes directly to entropy.

Non-Isothermal Process Integration

When a system undergoes a temperature change during heat transfer, the entropy change must be computed through integration, accounting for the fact that the temperature is not constant. Approaches may include using an average temperature or performing an integration if the specific temperature dependence is known.

Entropy

Entropy is a thermodynamic quantity that measures the degree of disorder or randomness in a system. It is also interpreted as a measure of how energy is dispersed at a specific temperature, central to the second law of thermodynamics.

Heat Transfer

Heat transfer refers to the energy that flows from a hot body to a colder one due to a temperature difference. In thermodynamics, the nature, amount, and path of heat transfer are key factors in determining the change in a system’s entropy.

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