Calculate the values of the molar heat capacities Cv and Cp of a gas,if the ratio of the heat capacities is 1.33.What is the atomicity of the gas?Given R=8.31J/mol-k.

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Calculate the values of the molar heat capacities Cv and Cp of a gas,if the ratio of the heat capacities is 1.33.What is the atomicity of the gas?Given R=8.31J/mol-k.

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Answer 1 · 2018-06-08T14:35:15

$\frac{C_{p}}{C_{v}} = γ$ $("C"_"p")/("C"_"v") = gamma$
$C_{p} - C_{v} = R$ $"C"_"p" - "C"_"v" = "R"$

From above two equations

$C_{p} = \frac{R γ}{γ - 1}$ $"C"_"p" = ("R" gamma)/(gamma - 1)$

$C_{p} = \frac{8.314 \times 1.33}{1.33 - 1}$ $color(white)("C"_"p") = "8.314 × 1.33"/(1.33 - 1)$

$C_{p} = 33.5 J/mol K$ $color(white)("C"_"p") = "33.5 J/mol K"$

$C_{v} = \frac{C_{p}}{γ}$ $"C"_"v" = "C"_"p"/gamma$

$C_{v} = \frac{33.5 J/mol K}{1.33}$ $color(white)("C"_"v") = "33.5 J/mol K"/"1.33"$

$C_{v} = 25.2 J/mol K$ $color(white)("C"_"v") = "25.2 J/mol K"$

$γ$ $gamma$ is $1.33$ $1.33$ therefore it’s triatomic (Atomicity $= 3$ $= 3$ ) gas.

$underline(bb"Type of gas" color(white)(............) bb(gamma)color(white)(....))$
$"Monoatomic" color(white)(000=) 1.66$
$"Diatomic" color(white)(..............) 1.40$
$"Triatomic" color(white)(......!!!!!!) 1.33$

Answer 2 · 2018-06-08T14:53:00

See below

Explanation:

Generally:

$c_p - c_v = R$

Here:

$c_p/c_v = 4/3$

$implies c_v = 3R, qquad c_p = 4R$

We know:

$c_p/c_v = (5 R + 2X)/(3 R + 2X)$
$X = {(0 qquad qquad "monatomic"),(R qquad qquad "diatomic"),(3/2 R qquad qquad "polyatomic"):}$

$4/3 = 8/6 = (5 + 2 * 3/2)/(3 + 3 * 3/2)$

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Calculate the values of the molar heat capacities Cv and Cp of a gas,if the ratio of the heat capacities is 1.33.What is the atomicity of the gas?Given R=8.31J/mol-k.

2 Answers

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