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  • Let  denote molar heat capacities of an ideal gas at constant volume and constant pres

Let C_p\: \: and\: \: C_v denote molar heat capacities of an ideal gas at constant volume and constant pressure respectively. Which of the following is universal constant?

Option: 1

\frac{C_p}{C_v}


Option: 2

C_p.C_v


Option: 3

C_p-C_v


Option: 4

C_p+C_v


Answers (1)

best_answer

As we learnt

 

Relation Between Cp And Cv -

For one mole of a gas Cp and Cv are known as molar heat capacities and the difference between them is equal to the work done by one mole of gas in expansion on heating it through 1oC.

constant pressure work done by the gas \mathrm{= P\Delta V}

For one mole of gas PV = RT

\begin{array}{l}{\text { On increasing temperature by } 1^{\circ} \mathrm{C}, \text { the volume }} \\ {\text { becomes } \mathrm{V}+\Delta \mathrm{V}} \\ {\text { Hence } \mathrm{P}(\mathrm{V}+\Delta \mathrm{V})=\mathrm{R}(\mathrm{T}+1)} \\ {\text { or } \mathrm{P} \Delta \mathrm{V}=\mathrm{R}} \\ {\text { that is, } \quad \mathrm{C}_{\mathrm{P}}-\mathrm{C}_{\mathrm{v}}=\mathrm{P} \Delta \mathrm{V}=\mathrm{R}}\end{array}

-

Relation between C(p) and C(v) -

C_{P}-C_{V}= R
- wherein

dH= dE+nR\, dT

\frac{dH}{ndT}= \frac{dE}{ndT}+R

C_{p}= C_{v}+R

C_{p}- C_{v}=R

R is a universal constant

Therefore, Option(3) is correct

Posted by

Divya Prakash Singh

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