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): \(\frac{n}{n+2}\)
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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.