For hydrogen gas Cp-Cv=a and for oxygen gas Cp-Cv=b, The relation between a and b is given by (A

step 1 Hello friends in the question it is given that for hydrogen gas Cp minus Cv is equal to A for hy

For hydrogen gas Cp-Cv=a and for oxygen gas Cp-Cv=b, The...

For hydrogen gas $\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}=\mathrm{a}$ and for oxygen gas $\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}=\mathrm{b}$, The relation between $\mathrm{a}$ and $\mathrm{b}$ is given by (A) $a=4 b$ (B) $a=b$ (C) $\mathrm{a}=16 \mathrm{~b}$ (D) $a=8 b$

For hydrogen gas $\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}=\mathrm{a}$ and for oxygen gas $\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}=\mathrm{b}$, The relation between $\mathrm{a}$ and $\mathrm{b}$ is given by
(A) $a=4 b$
(B) $a=b$
(C) $\mathrm{a}=16 \mathrm{~b}$
(D) $a=8 b$

Key Concepts

Specific Heat Capacities

This concept involves the heat capacities at constant pressure (C?) and constant volume (C?), which quantify the amount of heat required to raise the temperature of a given amount of substance by one degree under constant pressure or volume, respectively. The difference between these quantities is linked to the work done by the gas during expansion or compression.

Ideal Gas Behavior

Ideal gas behavior refers to the simplified model where gases are assumed to consist of non-interacting particles with negligible volume, obeying the ideal gas law (PV = nRT). This model allows derivation of relationships between various thermodynamic quantities, including the specific heats.

Molar Gas Constant

The molar gas constant (R) is a universal constant that appears in the ideal gas law, relating pressure, volume, temperature, and the number of moles of a gas. It serves as a bridge between the microscopic behavior of gas molecules and their macroscopic properties.

Fundamental Relationship between Specific Heats

For any ideal gas, the difference between the specific heat at constant pressure and the specific heat at constant volume is equal to the molar gas constant (C? - C? = R). This relationship is independent of the molecular structure of the gas and is a direct consequence of the first law of thermodynamics and the work associated with gas expansion.

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