At 300^∘ C and 1 atm, estimate the speed of sound of (a)...

Key Concepts

Speed_of_Sound_in_Gases

The speed of sound in a gas is determined by how quickly pressure disturbances propagate through the medium. It is generally calculated using the formula c = sqrt(?RT/M), where ? represents the adiabatic index, R is the universal gas constant, T is the absolute temperature, and M is the molar mass of the gas. This formula reflects the interplay between the gas's thermodynamic properties and its molecular composition.

Temperature_Conversion

In problems involving gas properties, temperature must be expressed in absolute units (Kelvin) rather than Celsius. This conversion is crucial because thermodynamic equations and the formula for the speed of sound rely on absolute temperature scales, where T (in Kelvin) equals the Celsius temperature plus 273.15.

Adiabatic_Index_?

The adiabatic index, denoted as ?, is the ratio of specific heats (Cp/Cv) and plays a significant role in determining the speed of sound. It varies depending on the molecular structure of the gas (for example, diatomic versus monatomic gases) and affects how efficiently the gas can transmit pressure changes through compression and expansion.

Molar_Mass_and_Gas_Constant

The molar mass (M) of a gas significantly influences the speed of sound, as heavier molecules result in a lower speed due to increased inertia. Along with the universal gas constant (R), which relates energy scales to temperature, the molar mass is a key factor in determining the thermodynamic responses of the gas as indicated in the speed of sound formula.

Ideal_Gas_Assumption

Many problems concerning the speed of sound assume that the gases behave ideally. This assumption simplifies the analysis by allowing the use of the ideal gas law and related formulas, providing accurate approximations for the speed of sound under many common conditions while neglecting intermolecular forces and finite molecular sizes.

Transcript

00:01 So here in this problem we have to calculate the speed of sound at 20 degrees celsius temperature is given as 20 degrees celsius for five different gases so for the part a we have to calculate for hydrogen so this the basic equation to calculate the speed of sound is given by c is equals to under root k rt so first we'll be calculating the speed for hydrogen so it will be equals to under root k for hydrogen it is 1 .41 times r for hydrogen it is 4 124 jule over k g kelvin times t it is given as 20 degrees celsius but we have to convert this thing into kelvin so we'll get 293 kelvin we're going to simplify this and we'll get the value as 1 ,305 meter per second now next we have to solve it for methane sorry for helium for the b part we have to solve for helium so we'll use the same formula so speed of sound for helium in case of helium will be equals to under root k for helium it is 1 .66 times k r so r for helium is 2077 jule over k g kelvin times t is 293 kelvin so we'll get the value as 1 ,0005 median per second now next for the c part we have to solve it for methane that is ch4 so we'll be using the same formula that is c for ch4 will be equals to under root k for methane is 1 .31 times r for methane is 518 .3 jule over kg kelvin times t is 293 kelvin so we're going to simplify this and we'll get the value of ch4 as 446 meter per second now in the d part we have to solid for nitrogen so again we'll be using the same formula so c4 n2 will be equals to under root the value of a k for a nitrogen it is 1 .40 times r is 296 point 8 times t is 293 kelvin so we'll get the value as 349 meter per second now next we have to solid for in the d part sorry in the e part you have to solve it for co2 so same using the same formula c for co2 will be equals to under root k for co2 is 1 .29 times r is one one one eighty eight point nine and t is same that is 293 kelvin so we'll get the value as for c co2 as 290 267 meter per second so these are the results for different gases this one this one this is for ch4 this is for n2 and this is for co2 and this is for co2 so i hope you understood the problem...

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