A gaseous mixture consists of 7 g of nitrogen and 20 g of argon. Assume gases to be ideal. The

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A gaseous mixture consists of 7 g of nitrogen and 20 g of...

A gaseous mixture consists of $7 \mathrm{~g}$ of nitrogen and $20 \mathrm{~g}$ of argon. Assume gases to be ideal. The specific heat capacities $C_{V}$ and $C_{P}$ in $\mathrm{J} / \mathrm{g}-\mathrm{K}$ for gaseous mixture are : (a) $C_{P}=0.66 \mathrm{~J} / \mathrm{g}-\mathrm{K}, \mathrm{C}_{V}=18.25 \mathrm{~J} / \mathrm{g}-\mathrm{K}$ (b) $C_{P}=1.66 \mathrm{~J} / \mathrm{g}-\mathrm{K}, \mathrm{C}_{V}=1.82 \mathrm{~J} / \mathrm{g}-\mathrm{K}$ (c) $C_{P}=0.421 \mathrm{~J} / \mathrm{g}-\mathrm{K}, \mathrm{C}_{V}=15.2 \mathrm{~J} / \mathrm{g}-\mathrm{K}$ (d) $C_{P}=0.65 \mathrm{~J} / \mathrm{g}-\mathrm{K}, \mathrm{C}_{V}=0.421 \mathrm{~J} / \mathrm{g}-\mathrm{K}$

A gaseous mixture consists of $7 \mathrm{~g}$ of nitrogen and $20 \mathrm{~g}$ of argon. Assume gases to be ideal. The specific heat capacities $C_{V}$ and $C_{P}$ in $\mathrm{J} / \mathrm{g}-\mathrm{K}$ for gaseous mixture are :
(a) $C_{P}=0.66 \mathrm{~J} / \mathrm{g}-\mathrm{K}, \mathrm{C}_{V}=18.25 \mathrm{~J} / \mathrm{g}-\mathrm{K}$
(b) $C_{P}=1.66 \mathrm{~J} / \mathrm{g}-\mathrm{K}, \mathrm{C}_{V}=1.82 \mathrm{~J} / \mathrm{g}-\mathrm{K}$
(c) $C_{P}=0.421 \mathrm{~J} / \mathrm{g}-\mathrm{K}, \mathrm{C}_{V}=15.2 \mathrm{~J} / \mathrm{g}-\mathrm{K}$
(d) $C_{P}=0.65 \mathrm{~J} / \mathrm{g}-\mathrm{K}, \mathrm{C}_{V}=0.421 \mathrm{~J} / \mathrm{g}-\mathrm{K}$

Key Concepts

Ideal Gas Behavior

This concept assumes that the gas molecules do not interact and occupy negligible volume compared to the container. It simplifies calculations of thermodynamic properties by applying the ideal gas law (PV = nRT), which is crucial when determining specific heat capacities and other properties of gas mixtures.

Specific Heat Capacities (C_P and C_V)

Specific heat at constant pressure (C_P) and at constant volume (C_V) are measures of the amount of energy required to raise the temperature of a substance by one degree under constant pressure or volume conditions, respectively. For gases, these capacities are linked to molecular motion and degrees of freedom, and they play a key role in understanding energy changes during thermodynamic processes.

Relation Between C_P and C_V

In ideal gases, there is a fundamental relation between the specific heats given by C_P - C_V = R (or a mass-based equivalent), where R is the gas constant. This relationship helps in deriving one specific heat capacity if the other is known and is essential in analyzing the energy exchange in processes involving ideal gases.

Mixture Property Calculations

When dealing with a gas mixture, properties such as specific heat capacities are calculated by considering the contributions of each component. This often involves using weighted averages based on mass or mole fractions, which allows for the determination of overall mixture properties from the individual component properties.

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