Physics · Kinetic Theory · NEET
Gamma is simply how many times bigger Cp is than Cv for the same gas. Cp is the heat needed to raise 1 mole by 1 K at constant pressure; Cv is the same at constant volume. Gamma is a single number that captures the nature of the gas (how many degrees of freedom it has), and it appears directly in adiabatic processes (PV^γ = constant) and in the speed of sound. That is why NEET keeps testing it.
Because Cp is always larger than Cv. At constant volume all the heat goes into raising internal energy. At constant pressure the gas also expands and does work, so you must supply extra heat (Mayer's relation: Cp - Cv = R). Since Cp > Cv, the ratio Cp/Cv is always more than 1. It can never equal 1 or be less.
Use γ = 1 + 2/f. Here f is the number of active degrees of freedom per molecule. Cv = (f/2)R and Cp = Cv + R = (f/2 + 1)R, so γ = Cp/Cv = (f + 2)/f = 1 + 2/f. Just count f, plug in, done. Monatomic f=3, diatomic (rigid) f=5, nonlinear polyatomic f=6.
A bigger f means the molecule has more ways to store energy (rotation, vibration), so 2/f becomes a smaller number, and γ = 1 + 2/f moves closer to 1. Monatomic (f=3): γ = 1.67. Diatomic (f=5): γ = 1.40. Polyatomic (f=6): γ = 1.33. More complexity, smaller gamma.
A rigid diatomic gas has f = 5 and γ = 7/5 = 1.40. If vibration becomes active, each vibrational mode adds 2 to f, so one vibrational mode gives f = 7 and γ = 1 + 2/7 = 9/7 ≈ 1.29. This exact idea was tested in NEET 2024 for a diatomic gas X with an extra vibrational mode.
You cannot just average the gammas. Add the Cv values weighted by moles: Cv(mix) = (n1·Cv1 + n2·Cv2)/(n1+n2). Then Cp(mix) = Cv(mix) + R, and γ(mix) = Cp(mix)/Cv(mix). Always work through Cv first, then take the ratio.
The values of Cp/Cv for hydrogen, helium and another ideal diatomic gas X (whose molecules are not rigid but have an additional vibrational mode) are respectively equal to:
An ideal gas is made of polyatomic molecules. Each molecule has three translational, three rotational and f vibrational modes. If the ratio of heat capacities Cp/Cv of the gas is 8/7, then the value of f is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Monatomic (He, Ar): γ = 5/3 ≈ 1.67. Rigid diatomic (H2, O2, N2): γ = 7/5 = 1.40. Nonlinear polyatomic (like CO2 bent, or f=6): γ = 4/3 ≈ 1.33.
Gamma is Cp divided by Cv (Cp/Cv). Since Cp is the larger one, this ratio is always greater than 1. Writing it as Cv/Cp is wrong and would give a value less than 1.
γ = 1 + 2/f, where f is the number of active degrees of freedom per molecule. Equivalently γ = (f + 2)/f.
No. Because Cp - Cv = R is positive, Cp is always more than Cv, so γ is always strictly greater than 1. The largest common value is 5/3 for monatomic gases.
It appears in adiabatic processes (PV^γ = constant, TV^(γ-1) = constant), in the speed of sound in a gas, and in specific-heat problems. NEET tests it almost every year, often by mixing up monatomic and diatomic values.
