Advertisements
Advertisements
प्रश्न
During an adiabatic process, the pressure of a mixture of monatomic and diatomic gases is found to be proportional to the cube of the temperature. Find the value of γ = `("C"_"P"/"C"_"V")`
उत्तर
In an adiabatic process, `"T"^γ"P"^(1 - γ)` = constant
`"P" ∝ "T"^3`
PT−3 = constant .........(1)
`"PT"^(γ/(1 - γ))` = constant ......(2)
`"PT"^(γ/(1 - γ)) = "PT"^-3`
Comparing the powers, `γ/(1 - γ)` = − 3 = − 3 + 3γ
2γ = 3
γ = `3/2`
APPEARS IN
संबंधित प्रश्न
A container has one mole of the monoatomic ideal gas. Each molecule has f degrees of freedom. What is the ratio of γ = `"C"_"p"/"C"_"v"`?
A sample of gas consists of μ1 moles of monoatomic molecules, μ2 moles of diatomic molecules and μ3 moles of linear triatomic molecules. The gas is kept at a high temperature. What is the total number of degrees of freedom?
Describe the total degrees of freedom for monoatomic molecule, diatomic molecule and triatomic molecule.
Derive the ratio of two specific heat capacities of monoatomic, diatomic and triatomic molecules.
Which of the following statement given below are correct for monoatomic gas?
I. Cv = `3/2 "R"`
II. Cp = `5/2 "R"`
III. Cp − Cv = 2R
IV. `"C"_"p"/"C"_"v" = 5/3`
A ballon has 5.0 g mole of helium at 7°C. Calculate
- the number of atoms of helium in the balloon
- the total internal energy of the system.
Calculate the number of degrees of freedom of molecules of hydrogen in 1 cc of hydrogen gas at NTP.
Which statements are correct about degrees of freedom?
- A molecule with n degrees of freedom has n2 different ways of storing energy.
- Each degree of freedom is associated with `1/2`RT average energy per mole.
- A monoatomic gas molecule has 1 rotational degree of freedom whereas the diatomic molecule has 2 rotational degrees of freedom.
- CH4 has a total of 6 degrees of freedom.
Choose the correct answer from the option given below:
A gas has n degrees of freedom. The ratio of the specific heat of the gas at constant volume to the specific heat of the gas at constant pressure will be ______.
An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (CP) and at constant volume (Cv) is ______.
