Specific Heat of an Ideal Gas: Temperature vs. Molecular Weight and Structure

In summary: For a diatomic molecule, the vibrational modes can be excited if the molecular temperature is above 600 K. For a monatomic gas, there are no vibrational modes, only translational modes, and Cv is 3R.
  • #1
Monsterboy
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Homework Statement


Does the specific heat of an ideal gas depend on the temperature only or does it depend on molecular weight and structure ? or both ?

Homework Equations


PV=mRT , Cp -Cv=R

The Attempt at a Solution


One of my teachers said it depends only on temperature and the other said it depends on molecular weight and structure ,i am not sure who is correct ,is it possible to find out who is correct by using the above equations ?

Cv( ##\gamma## -1) = R

PV=RT

PV/T = R = Cv(##\gamma## -1)

##\gamma## -1 = PV/TCv

I don't know how to proceed.
 
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  • #2
Monsterboy said:

Homework Statement


Does the specific heat of an ideal gas depend on the temperature only or does it depend on molecular weight and structure ? or both ?

Homework Equations


PV=mRT , Cp -Cv=R

The Attempt at a Solution


One of my teachers said it depends only on temperature and the other said it depends on molecular weight and structure ,i am not sure who is correct ,is it possible to find out who is correct by using the above equations ?

Cv( ##\gamma## -1) = R

PV=RT

PV/T = R = Cv(##\gamma## -1)

##\gamma## -1 = PV/TCv

I don't know how to proceed.
It's both. Sometimes physicists talk about perfect gases, for which heat capacity is considered independent of temperature, and sometimes they refer to such gases as ideal gases. Engineers regard the heat capacity of ideal gases as temperature-dependent because real gases approach this behavior in the limit of low pressures (ideal gas limit). For an engineer, the ideal gas heat capacity varies with temperature exactly as the actual gas heat capacity varies (experimentally) in the limit of low pressures.

Ideal gas heat capacity is affected by structure because polyatomic molecules are capable of exhibiting vibrational and rotational energy accumulation.
 
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  • #3
Chestermiller said:
It's both. Sometimes physicists talk about perfect gases, for which heat capacity is considered independent of temperature, and sometimes they refer to such gases as ideal gases. Engineers regard the heat capacity of ideal gases as temperature-dependent because real gases approach this behavior in the limit of low pressures (ideal gas limit). For an engineer, the ideal gas heat capacity varies with temperature exactly as the actual gas heat capacity varies (experimentally) in the limit of low pressures.

Ideal gas heat capacity is affected by structure because polyatomic molecules are capable of exhibiting vibrational and rotational energy accumulation.

Ok , is it possible to know which factor affects the specific heat more ? is it possible to ignore any of them in engineering point of view ?
Actually for the question i have ,there are four options
A . Temperature B. Is not affected by either
C.Volume D. Molecular weight and structure.

so the answer is A and D ? but this option is not given
 
  • #4
Monsterboy said:
Ok , is it possible to know which factor affects the specific heat more ?
Typically, structure more than temperature.
is it possible to ignore any of them in engineering point of view ?
Often, the temperature dependence can be ignored (over limited ranges of temperature).
Actually for the question i have ,there are four options
A . Temperature B. Is not affected by either
C.Volume D. Molecular weight and structure.

so the answer is A and D ? but this option is not given
Yes, the answer is A and D. But, if this is being taught by Physicists, they may not count A.
 
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  • #5
In an ideal gas, molecules are considered as point masses without any dimensions right ? so how is structure considered as a factor here ?
 
  • #6
Monsterboy said:
In an ideal gas, molecules are considered as point masses without any dimensions right ? so how is structure considered as a factor here ?
Ideal gas is assumed to consist of non-interacting particles of negligible size with respect to the size of the container. Still, they have structure, moment of inertia, so they have rotational energy in addition to the translational kinetic energy. That is why at about room temperature, Cv of the two-atomic gases is 5/2 R and 3R if the molecules consist of three or more atoms. The molecules also vibrate, and the vibration modes become excited at higher temperatures, making Cv increasing with the temperature.
 
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FAQ: Specific Heat of an Ideal Gas: Temperature vs. Molecular Weight and Structure

What is specific heat?

Specific heat is the amount of heat energy required to raise the temperature of a unit mass of a substance by 1 degree Celsius.

What is the specific heat of an ideal gas?

The specific heat of an ideal gas is the amount of heat energy required to raise the temperature of a unit mass of the gas by 1 degree Celsius at constant pressure.

How is specific heat of an ideal gas calculated?

The specific heat of an ideal gas can be calculated using the formula C = (5/2)R, where C is the specific heat, and R is the universal gas constant.

What factors affect the specific heat of an ideal gas?

The specific heat of an ideal gas is affected by the type of gas, temperature, and pressure. It also depends on whether the process is taking place at constant volume or constant pressure.

Why is specific heat important?

Specific heat is important because it allows us to calculate the amount of heat energy required to change the temperature of a substance. It is also used in various thermodynamic equations and plays a crucial role in understanding the behavior of gases.

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