Question

$\mathrm{Cp}$ and Cv denote the specific heat of oxygen per unit mass at constant Pressure and volume respectively, then (A) $\mathrm{cp}-\mathrm{cv}=(\mathrm{R} / 16)$ (B) $\mathrm{Cp}-\mathrm{Cv}=\mathrm{R}$ (C) $\mathrm{Cp}-\mathrm{Cv}=32 \mathrm{R}$ (D) $\mathrm{Cp}-\mathrm{Cv}=(\mathrm{R} / 32)$

Name: Problem 1123, Chapter 8: JEE Physics
Uploaded: 2021-09-30T17:20:35-08:00
Duration: 1 min 51 s
Channel: Sachin Rao
Description: Cp and Cv denote the specific heat of oxygen per unit mass at constant Pressure and volume respectively, then (A) cp-cv=(R / 16) (B) Cp-Cv=R (C) Cp-Cv=32 R (D) Cp-Cv=(R / 32)

   $\mathrm{Cp}$ and Cv denote the specific heat of oxygen per unit mass at constant Pressure and volume respectively, then
(A) $\mathrm{cp}-\mathrm{cv}=(\mathrm{R} / 16)$
(B) $\mathrm{Cp}-\mathrm{Cv}=\mathrm{R}$
(C) $\mathrm{Cp}-\mathrm{Cv}=32 \mathrm{R}$
(D) $\mathrm{Cp}-\mathrm{Cv}=(\mathrm{R} / 32)$

JEE Physics

StemEZ 1st Edition

Chapter 8, Problem 1123

Instant Answer

Solved by Expert Sachin Rao

09/30/2021

Step 1

We know that the relation between Cp and Cv is given by the equation: \[Cp - Cv = R\] where R is the gas constant. Show more…

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$\mathrm{Cp}$ and Cv denote the specific heat of oxygen per unit mass at constant Pressure and volume respectively, then (A) $\mathrm{cp}-\mathrm{cv}=(\mathrm{R} / 16)$ (B) $\mathrm{Cp}-\mathrm{Cv}=\mathrm{R}$ (C) $\mathrm{Cp}-\mathrm{Cv}=32 \mathrm{R}$ (D) $\mathrm{Cp}-\mathrm{Cv}=(\mathrm{R} / 32)$

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Key Concepts

Specific Heats in Ideal Gases

In thermodynamics for an ideal gas, the specific heat at constant pressure (cp) and the specific heat at constant volume (cv) are related by the equation cp - cv = R_specific. This relationship comes from the first law of thermodynamics and the work done during expansion at constant pressure, leading to the additional energy required per unit mass.

Gas Constant and Molar Mass

The specific gas constant (R_specific) for a substance is obtained by dividing the universal gas constant (R_universal) by the molar mass of the gas. For any gas, this conversion is crucial when dealing with properties defined per unit mass rather than per mole; for example, using oxygen's molecular mass in the conversion yields the proper relation between cp and cv.

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