During an adiabatic process,the pressure of a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) For an adiabatic process,the relation between pressure $p$ and volume $V$ is given by $pV^\gamma = k$,where $\gamma = C_p / C_V$ is the adiabatic

Vedclass · Accepted Answer

$3/2$

Vedclass · Answer

(D) For an adiabatic process,the relation between pressure $p$ and volume $V$ is given by $pV^\gamma = k$,where $\gamma = C_p / C_V$ is the adiabatic index. $(i)$Given that $p \propto T^3$,we can write $p = k' T^3$,where $k'$ is a constant.Using the ideal gas equation $pV = nRT$,we have $T = \frac{pV}{nR}$.Substituting this into the given relation:$p = k' \left( \frac{pV}{nR} ight)^3$$p = \left( \frac{k'}{n^3 R^3} ight) p^3 V^3$$1 = \left( \frac{k'}{n^3 R^3} ight) p^2 V^3$$p^2 V^3 = 	ext{constant}$$p V^{3/2} = 	ext{constant}$ (ii)Comparing equation $(i)$ and (ii),we get $\gamma = 3/2$.Therefore,the value of $C_p / C_V$ is $3/2$.

During an adiabatic process,the pressure of a gas is proportional to the cube of its temperature. The value of $C_p / C_V$ for that gas is

Similar Questions

The pair not correctly matched is

The area (in sq units) of the triangle formed by the tangent at $(\sqrt{3}, 0)$ to the hyperbola $x^2-3y^2=3$ with the pair of asymptotes of the hyperbola is

Which of the following factors exclusively affects reproduction in seasonal breeders,both plants and animals?

Which one of the following precedes the re-formation of the nuclear envelope during the $M$ phase of the cell cycle?

Vedclass Test Series

Exam Paper Generator

Online Exam Module