The temperature of 1.00 mol of a monatomic ideal gas is raised reversibly from 300 K to 400 K

step 1 For this problem on the topic of entropy, we are told that the temperature of a mole of a monoto

The temperature of 1.00 mol of a monatomic ideal gas is...

The temperature of $1.00 \mathrm{~mol}$ of a monatomic ideal gas is raised reversibly from $300 \mathrm{~K}$ to $400 \mathrm{~K},$ with its volume kept constant. What is the entropy change of the gas?

Key Concepts

Entropy Change

Entropy is a state function that quantifies the degree of disorder or randomness within a system, and its change during a process provides insight into the direction and spontaneity of that process. The entropy change in a system during a reversible process is determined by integrating the infinitesimal heat added divided by the temperature at which it is added, which simplifies to analytical expressions under constant conditions such as constant volume or pressure.

Molar Heat Capacity

Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one degree under specified conditions. In the context of constant volume processes for gases, the molar heat capacity at constant volume, often denoted by Cv, plays a critical role in relating changes in temperature to changes in internal energy and entropy.

Isochoric Process

An isochoric process, also known as a constant volume process, is a type of thermodynamic process in which the volume of the system remains unchanged. In such processes, no work is done by the system because work in thermodynamics is often associated with volume change. Instead, any heat added or removed only changes the internal energy and temperature of the system.

Ideal Gas

An ideal gas is a theoretical model of a gas composed of a large number of small particles that move in random motion and do not interact except through elastic collisions. Ideal gases strictly follow the ideal gas law, which simplifies the analysis of thermodynamic processes by assuming no intermolecular forces and negligible molecular volume.

Reversible Process

A reversible process is an idealized thermodynamic process that occurs infinitely slowly, ensuring the system remains in near-equilibrium throughout the change. This concept is crucial for theoretical analyses, as reversible processes set the upper limit on the efficiency and maximum work obtained from a thermodynamic cycle.

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