Question

Help please. Will give fan and medal (:

Answer 1

The velocity v_sof sound within a gas is given by the subsequent formula:
\[{v_s} = \sqrt {\frac{{\gamma RT}}{M}} \]
where \gamma is a coefficient depending on the gas type, R is the gas constant, T is the absolute temperature, and M is the mass of one mole of that gas.

Answer 2

So for a more dense gas, its molecules have lower speed.

Answer 3

please wait, I'm searching for your answer, in my textbook

Answer 4

we have:
\[R = 8.31\quad J/\left( {K \cdot mol} \right)\]
is the gas constant

Answer 5

whereas \[\gamma >1\]
is another constant related to a specific gas. for example for the air we have:
\[\gamma = 1.4\]

Answer 6

M is the mass of a singl mole of our gas. Namely if N is the number of mole of our gas, and m is the mass of our gas, then we have:
\[M = \frac{m}{N}\]

Answer 7

finally, T is the absolute temperature of our gas.

Answer 8

if t= 0°C, then T = 273.15 K, furthermore, the mass of a molecule of air can be computed if we know the molecular composition of the air, I think that your value is right!

Answer 9

oops.. the mass of a mole of air...

Answer 10

furthermore, I remember, but I'm not sure, that the coefficient \[\gamma \]
is the ratio between the specific heat at constant pressure and the
specific heat at constant volume

Answer 11

please check my last statement

Answer 12

please, wait, the coefficient \[\gamma \], is the same coefficient which is present in the formula of adiabatic transformations, namely:

\[p{V^\gamma } = \cos t\]
in the pressures-volume plane, so now I'm sure that we have:
\[\gamma = \frac{{{c_p}}}{{{c_v}}}\]
as I said before.

Answer 13

we have to keep in mind that there is an important relationship between C_p and C_v, namely:
\[{C_p} - {C_v} = R\]

Answer 14

here are some values:

Answer 15

monatomic gases like He, Ar
\[{C_p} = 5,\quad {C_v} = 3,{\kern 1pt} \quad \gamma = 1.67\]

Answer 16

diatomic gases, like H2, N2, O2:
\[{C_p} = 7,\quad {C_v} = 5,{\kern 1pt} \quad \gamma = 1.40\]

Answer 17

triatomic gases like CO2:
\[{C_p} \sim 9,\quad {C_v} \sim 7,{\kern 1pt} \quad \gamma \sim 1.3\]

Answer 18

please note that all values are related to one mole of the gas, and their unit of measure is:
cal/(mol*K)

Answer 19

yes, one value of gamma for He, and another value of gamma, for CO2