Values of S^∘(Cu, s) at 400 K and 500 K are 40.5 and 46.2 JK^-1 mol^-1 respectively. Estimate th

Values of S^∘(Cu, s) at 400 K and 500 K are 40.5 and 46.2...

Values of $S^{\circ}(\mathrm{Cu}, \mathrm{s})$ at $400 \mathrm{K}$ and $500 \mathrm{K}$ are 40.5 and $46.2 \mathrm{JK}^{-1} \mathrm{mol}^{-1}$ respectively. Estimate the molar heat capacity of copper over this temperature range.

Key Concepts

Thermodynamic Relation between Entropy and Temperature

The relationship dS = Cp/T dT links changes in entropy to changes in temperature via the heat capacity. By integrating this expression over a given temperature range, one can estimate the average molar heat capacity if the change in entropy is known, thus bridging the concepts of entropy and energy absorption.

Molar Heat Capacity

Molar heat capacity represents the amount of heat required to raise the temperature of one mole of a substance by one degree Kelvin. It connects energy changes to temperature variations in a system and is a key thermodynamic property that helps describe how substances store thermal energy.

Entropy

Entropy is a thermodynamic state function that quantifies the disorder or randomness within a system. It is used to assess the distribution of energy at the molecular level and plays a critical role in determining the spontaneity of processes and the evolution of thermodynamic systems.

Transcript

00:01 In the given question, we have been provided a 25 gram of copper sample.

00:05 Okay, so the mass of copper is 25 gram.

00:09 We have been provided that the temperature of this copper is 363 kelvin.

00:16 It is placed in 100 gram water.

00:18 So mass of water is 100 gram.

00:22 And the temperature of water is provided us to be 293 kelvin.

00:27 We have been provided that copper and water came to same temperature after a heat transfer.

00:32 From copper to water, we have to calculate the final temperature of water.

00:38 Okay.

00:40 And we have been provided that the molar heat capacity of copper is, okay, copper's molar heat capacity is 24 .5 joule kelvin inverse, mole inverse.

00:54 And for water, this is provided to be 75 .2 joule kelvin inverse, mole inverse.

01:02 Okay.

01:02 So we have to find the final temperature of water and we have been provided initial temperature of copper and the initial temperature of water.

01:10 So how we can do this question? we know that whenever two substances with different temperature are kept together, then there is heat flow.

01:19 So the heat absorbed by water will be equal to heat transfer by copper.

01:31 Okay.

01:33 So we can use the formula.

01:35 Okay.

01:35 So heat absorbed by water will be equals to moles of water into sea of water into change in temperature for water.

01:46 Okay.

01:46 So this side i'm writing for water.

01:48 So this is nc delta t.

01:52 And for copper, it will be negative since it is releasing the heat...

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