What is Gamma (Cp/Cv)? Values for Monatomic and Diatomic Gases
Physics · Thermodynamics · NEET
Gamma (written as the Greek letter, and called the ratio of specific heats or adiabatic exponent) is defined as gamma = Cp / Cv, where Cp and Cv are the molar specific heats at constant pressure and constant volume. Its value is always greater than 1 because Cp is always greater than Cv. Memory hook: for a monatomic gas gamma = 5/3 (about 1.67) and for a diatomic gas gamma = 7/5 (1.4) - think "atoms fewer, gamma higher".
Gamma = Cp/Cv for the three gas types. As degrees of freedom f rise from 3 to 5 to 6, gamma falls from 5/3 to 7/5 to 4/3, following the shortcut gamma = 1 + 2/f.
Your doubts, answered
Is gamma always greater than 1?
Yes. Gamma = Cp / Cv, and Cp is always larger than Cv (Mayer's relation Cp - Cv = R, with R positive). So the numerator is always bigger than the denominator, which makes gamma greater than 1 for every ideal gas. You will never get a correct value of gamma less than or equal to 1.
Why is gamma = 5/3 for a monatomic gas?
A monatomic gas (like helium or argon) has 3 degrees of freedom, all translational. So Cv = (3/2)R and Cp = Cv + R = (5/2)R. Then gamma = Cp / Cv = (5/2)R divided by (3/2)R = 5/3, which is about 1.67.
Why is gamma = 7/5 for a diatomic gas?
A diatomic gas (like oxygen or nitrogen) at ordinary temperature has 5 degrees of freedom (3 translational + 2 rotational). So Cv = (5/2)R and Cp = (7/2)R. Then gamma = (7/2)R divided by (5/2)R = 7/5 = 1.4.
What is the shortcut formula for gamma using degrees of freedom?
If f is the number of degrees of freedom, then gamma = 1 + 2/f. Check: monatomic f = 3 gives gamma = 1 + 2/3 = 5/3. Diatomic f = 5 gives gamma = 1 + 2/5 = 7/5. This formula is the fastest way to get gamma in an exam.
Does gamma have any units?
No. Gamma is a pure ratio of two specific heats that have the same units, so the units cancel. It is a dimensionless number. That is why you can compare gamma across different gases directly.
⚠️ The NEET trap ✗ Using gamma = Cv / Cp, which gives a value less than 1 (like 3/5 or 5/7). ✓ Gamma = Cp / Cv, which is always greater than 1 (monatomic 5/3, diatomic 7/5). Cp is on top because it is the larger value. 🧠 Gamma is the BIG heat over the small heat. If your answer is less than 1, you flipped the fraction.
Real NEET questions
ReNEET 2026
In an adiabatic expansion, the temperature of one mole of an ideal monatomic gas (gamma = 5/3) decreases from 60 K to 50 K. The work done by the gas in the process is: [Take R = 8.3 J per mol per K]
A · 41.5 J
B · 83 J
C · 124.5 J ✓
D · 166 J
Solution: For an adiabatic process the work done by the gas is W = nR(T1 - T2) / (gamma - 1), which is the same as W = nR(delta T) / (1 - gamma).
Step 1: List values. n = 1, T1 = 60 K, T2 = 50 K, so delta T = 50 - 60 = -10 K, gamma = 5/3, R = 8.3.
Step 2: Compute gamma - 1 = 5/3 - 1 = 2/3.
Step 3: W = nR(T1 - T2) / (gamma - 1) = (1)(8.3)(60 - 50) / (2/3).
Step 4: Numerator = 8.3 x 10 = 83. Divide by 2/3 means multiply by 3/2: W = 83 x 3/2 = 124.5 J.
This question needs you to know gamma = 5/3 for a monatomic gas. Answer: C.
NEET 2018
The volume (V) of a monatomic gas varies with its temperature (T) as shown in the graph (a straight line through the origin, an isobaric process). The ratio of the work done by the gas to the heat absorbed by it, when it goes from A to B, is
A · 1/3
B · 2/3
C · 2/5 ✓
D · 2/7
Solution: Step 1: V is proportional to T (straight line through origin), so V/T is constant. By the ideal gas law this means pressure P is constant, so the process is isobaric.
Step 2: Work done in an isobaric process is W = P(delta V) = nR(delta T).
Step 3: Heat absorbed at constant pressure is Q = n Cp (delta T).
Step 4: Ratio W/Q = nR(delta T) / (n Cp delta T) = R / Cp.
Step 5: For a monatomic gas Cp = (5/2)R, so W/Q = R / ((5/2)R) = 2/5.
This uses the monatomic value Cp = (5/2)R that comes from gamma = 5/3. Answer: C.
Solved Thermodynamics NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Gamma is the ratio of the two molar specific heats, gamma = Cp / Cv. It is also called the adiabatic exponent because it appears in the adiabatic law P times V raised to the power gamma is constant.
What is the value of gamma for monatomic, diatomic and polyatomic gases?
Monatomic: gamma = 5/3 (about 1.67). Diatomic: gamma = 7/5 = 1.4. Non-linear polyatomic (like carbon dioxide bent shape, f = 6): gamma = 4/3 (about 1.33). As degrees of freedom increase, gamma decreases toward 1.
What is the relation between gamma and degrees of freedom?
Gamma = 1 + 2/f, where f is the number of degrees of freedom. More degrees of freedom means a value of gamma closer to 1.
Can gamma be equal to 1 or less than 1?
No. Since Cp is always greater than Cv, gamma is always greater than 1. A value of 1 or less means you made a mistake, usually by writing Cv/Cp instead of Cp/Cv.
Why is gamma important for adiabatic processes?
In an adiabatic process the state follows P times V raised to the power gamma equals constant. The size of gamma decides how steep the adiabatic curve is on a P-V graph compared to the isothermal curve.
