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Chapter 7: Problem 921

What is the ratio of the adiabatic to isothermal elasticities of a triatomic gas ? (A) \((3 / 4)\) (B) \((4 / 3)\) (C) 1 (D) \((5 / 3)\)

Short Answer

Expert verified
The ratio of the adiabatic to isothermal elasticities for a triatomic gas is \( \frac{7}{5} \). However, this option is not available in the given choices. There may be an error in the question or the options.

Step by step solution

01

Find the Degrees of Freedom for Triatomic Gas

A triatomic gas has 3 translational and 2 rotational degrees of freedom. Therefore, it has a total of 3 + 2 = 5 degrees of freedom.
02

Calculate Heat Capacity at Constant Volume (Cv)

We calculate Cv using the formula: Cv = (f/2)R, where f is the degrees of freedom, and R is the gas constant. Here, f = 5. Cv = \(\frac{5}{2}\)R
03

Calculate Heat Capacity at Constant Pressure (Cp)

We calculate Cp using the formula: Cp = Cv + R. Cp = \(\frac{5}{2}\)R + R = \(\frac{7}{2}\)R
04

Calculate Adiabatic Elasticity (Cp / Cv)

The adiabatic elasticity is the ratio of Cp to Cv: Adiabatic Elasticity = \( \frac{Cp}{Cv} = \frac{\frac{7}{2}R}{\frac{5}{2}R} \)
05

Simplify the Adiabatic Elasticity

Cancel out the common factor R and simplify: Adiabatic Elasticity = \( \frac{7}{5} \)
06

Calculate Isothermal Elasticity

Isothermal elasticity is always equal to 1 for an ideal gas.
07

Find the Ratio of Adiabatic to Isothermal Elasticity

The ratio of the adiabatic to isothermal elasticity is \( \frac{7}{5} \) divided by 1: Ratio = \( \frac{7}{5} \) Comparing the given options, the answer is not available in the list. There may be an error in the question or the options.

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Most popular questions from this chapter

The ratio of two specific heats of gas $\mathrm{C}_{\mathrm{P}} / \mathrm{C}_{\mathrm{V}}\( for Argon is \)1.6\( and for hydrogen is \)1.4 .$ Adiabatic elasticity of Argon at pressure P is E. Adiabatic elasticity of hydrogen will also be equal to \(\mathrm{E}\) at the pressure. (A) \(\mathrm{P}\) (B) \((7 / 8) \mathrm{P}\) (C) \((8 / 7) \mathrm{P}\) (D) \(1.4 \mathrm{P}\)

Read the assertion and reason carefully and mark the correct option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. Assertion: Tiny drops of liquid resist deforming forces better than bigger drops. Reason: Excess pressure inside a drop is directly proportional to surface tension. (A) a (B) \(b\) (C) (D) d

Maximum density of \(\mathrm{H}_{2} \mathrm{O}\) is at the temperature. (A) \(32^{\circ} \mathrm{F}\) (B) \(39.2^{\circ} \mathrm{F}\) (C) \(42^{\circ} \mathrm{F}\) (D) \(4^{\circ} \mathrm{F}\)

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Radius of a soap bubble is \(\mathrm{r}^{\prime}\), surface tension of soap solution is \(\mathrm{T}\). Then without increasing the temperature how much energy will be needed to double its radius. (A) \(4 \pi r^{2} T\) (B) \(2 \pi r^{2} T\) (C) \(12 \pi r^{2} T\) (D) \(24 \pi r^{2} T\)
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