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Chapter 8: Problem 1100

If for a gas $\left(\mathrm{C}_{\mathrm{p}} / \mathrm{C}_{\mathrm{v}}\right)=1.67$, this gas is made up to molecules which are (A) diatomic (B) Polytomic (C) monoatomic (D) mixnese of diatomic and polytomic molecules

Short Answer

Expert verified
The given ratio of specific heat capacities, γ = 1.67, matches with the value for monoatomic gases. Therefore, the gas is made up of \( \textbf{monoatomic} \) molecules.

Step by step solution

01

Understand the terms

In this exercise, we're dealing with the ratio of C_p and C_v for a gas, which are called specific heat capacities. Specific heat capacities are related to the ability of a substance to absorb heat and change temperature. The ratio we are working with is often denoted as γ (gamma). For a gas, we have: γ = C_p / C_v The values of C_p and C_v depend on the type of molecules present in the gas (monoatomic, diatomic, or polyatomic).
02

Relate the γ values to the type of gas molecules

The ratio of specific heat capacities (γ) for different types of gas molecules is: 1. Monoatomic gases (such as He, Ne, Ar): γ = 5/3 ≈ 1.67 2. Diatomic gases (such as H2, N2, O2): γ = 7/5 ≈ 1.4 3. Polytomic gases (such as H2O, CO2, NO2): γ < 1.4 Comparing the given value γ=1.67 with the above values for different types of molecules, we can see that the ratio matches with the value for monoatomic gases.
03

Choose the correct answer

Since the given ratio (1.67) matches the value for monoatomic gases, we can conclude that the gas is made up of monoatomic molecules. Therefore, the correct answer is: (C) monoatomic

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