ΔS=(qm)/(T1)+c ln(T2)/(T)+(qv)/(T2) =(333)/(273)+4 ·18 ln(373)/(283) ∼8.56 J / ^∘ K

Name: Problem 214, Chapter 2: Solutions to I.E. Irodov's problems in general physics
Uploaded: 2021-08-23T13:56:20-08:00
Duration: 2 min 25 s
Channel: Ajay Singhal
Description: ΔS=(qm)/(T1)+c ln(T2)/(T)+(qv)/(T2) =(333)/(273)+4 ·18 ln(373)/(283) ∼8.56 J / ^∘ K

step 1 Hello students in this question we have an ice which is initially at a temperature T1 equals to

ΔS=(qm)/(T1)+c ln(T2)/(T)+(qv)/(T2) =(333)/(273)+4...

$$
\begin{aligned}
\Delta S=\frac{q_{m}}{T_{1}}+c \ln \frac{T_{2}}{T}+\frac{q_{v}}{T_{2}} & \\
&=\frac{333}{273}+4 \cdot 18 \ln \frac{373}{283} \sim 8.56 \mathrm{~J} /{ }^{\circ} \mathrm{K}
\end{aligned}
$$

Key Concepts

Specific Heat Capacity

Specific heat capacity refers to the quantity of energy required to raise the temperature of a unit mass of a substance by one degree. When calculating entropy changes during temperature variations, the specific heat capacity is used to determine the heat added or removed over a temperature range through integration.

Entropy

Entropy is a thermodynamic property that quantifies the degree of disorder or randomness in a system. It reflects how energy disperses among the available microstates and determines the direction of spontaneous processes, with the change in entropy indicating the system’s progression toward equilibrium.

Heat Transfer

Heat transfer is the process by which energy in the form of heat moves from one body or system to another due to a temperature difference. In thermodynamic calculations, heat transfer influences the change in entropy, with the amount of heat exchanged divided by the temperature providing a measure of the corresponding entropy change.

Integration Over Temperature

When a system undergoes a temperature change, the calculation of the associated entropy change involves integrating the heat capacity over the temperature range. This integration often results in a logarithmic expression, reflecting the cumulative effect of incremental temperature changes on the system’s entropy.

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