Calculate the change of entropy involved in heating a...

Calculate the change of entropy involved in heating a gram-atomic weight of silver at constant volume from $0^{\circ}$ to $30^{\circ} \mathrm{C}$. The value of $C_v$ over this temperature may be taken as a constant equal to $5.85 \mathrm{cal} / \mathrm{deg}$ mole.

Key Concepts

Entropy

Entropy is a thermodynamic state function that quantifies the degree of disorder or randomness in a system. It is defined through the relation dS = dQ/T, where dQ is the infinitesimal amount of heat added reversibly and T is the absolute temperature. This concept is crucial for understanding how energy disperses within a system during various thermodynamic processes.

Heat Capacity at Constant Volume (Cv)

Heat capacity at constant volume is the amount of heat required to raise the temperature of a given amount of substance by one degree while keeping the volume constant. It is used in thermodynamic calculations to determine internal energy changes during heating processes and is assumed constant over the temperature range of interest in many simplified problems.

Constant Volume Process

A constant volume process is one in which the volume of the system remains unchanged. In such processes, no work is done by the system on its surroundings because work expression involves changes in volume. As a result, any heat added to the system directly changes its internal energy, influencing the entropy change in thermal processes.

Integration in Thermodynamics

Integration is used in thermodynamics to calculate changes in state functions like entropy when the system undergoes a change in temperature. With a constant heat capacity, the integration of the differential form dS = Cv(dT/T) over a specified temperature range yields an expression for the entropy change in a process, highlighting the cumulative effect of incremental heat exchanges.

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