A gas has n degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be
- \(\frac{n}{n+2}\)
- \(\frac{n+2}{n}\)
- \(\frac{n}{2n+2}\)
- \(\frac{n}{n-2}\)
The Correct Option is A
Solution and Explanation
Ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure :
Specific heat of gas constant volume : \(C_v = \frac{nR}2\)
Again, Specific heat of gas at constant pressure : \(C_p = \frac{nR}{2+R}\)
\(⇒ \frac{C_v}{C_p}\)
= \(\frac{\frac{nR}{2}}{\frac{nR}{2+R}}\)
= \(\frac{n}{n+2}\)
Hence, the correct option is (A): \(\frac{n}{n+2}\)
Top Questions on Ideal gas equation
- What is the ideal gas law equation?
- MHT CET - 2025
- Chemistry
- Ideal gas equation
- Which of the following gases is most likely to deviate from ideal gas behavior at high pressures and low temperatures?
- MHT CET - 2025
- Chemistry
- Ideal gas equation
- A sample of gas occupies 10 L at 300 K and 2 atm. What will be its volume at 400 K and 1 atm?
- MHT CET - 2025
- Chemistry
- Ideal gas equation
- What is the molar volume of an ideal gas at standard temperature and pressure (STP)?
- VITEEE - 2025
- Chemistry
- Ideal gas equation
- A gas occupies 2 liters at a pressure of 3 atm. What will be its volume when the pressure is reduced to 1.5 atm at constant temperature?
- AP EAPCET - 2025
- Chemistry
- Ideal gas equation
Questions Asked in JEE Main exam
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?
- JEE Main - 2026
- Organic Chemistry
- Let \( ABC \) be an equilateral triangle with orthocenter at the origin and the side \( BC \) lying on the line \( x+2\sqrt{2}\,y=4 \). If the coordinates of the vertex \( A \) are \( (\alpha,\beta) \), then the greatest integer less than or equal to \( |\alpha+\sqrt{2}\beta| \) is:
- JEE Main - 2026
- Coordinate Geometry
- Three charges $+2q$, $+3q$ and $-4q$ are situated at $(0,-3a)$, $(2a,0)$ and $(-2a,0)$ respectively in the $x$-$y$ plane. The resultant dipole moment about origin is ___.
- JEE Main - 2026
- Electromagnetic waves
Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.- JEE Main - 2026
- Complex Numbers and Quadratic Equations
- The work functions of two metals ($M_A$ and $M_B$) are in the 1 : 2 ratio. When these metals are exposed to photons of energy 6 eV, the kinetic energy of liberated electrons of $M_A$ : $M_B$ is in the ratio of 2.642 : 1. The work functions (in eV) of $M_A$ and $M_B$ are respectively.
- JEE Main - 2026
- Dual nature of matter
Concepts Used:
Gas Laws
The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases.
The five gas laws are:
- Boyle’s Law, which provides a relationship between the pressure and the volume of a gas.
- Charles’s Law, which provides a relationship between the volume occupied by a gas and the absolute temperature.
- Gay-Lussac’s Law, which provides a relationship between the pressure exerted by a gas on the walls of its container and the absolute temperature associated with the gas.
- Avogadro’s Law, which provides a relationship between the volume occupied by a gas and the amount of gaseous substance.
- The Combined Gas Law (or the Ideal Gas Law), which can be obtained by combining the four laws listed above.