Question

During a reversible adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $\frac{C_p}{C_v}$ for the gas is ________.

• A. $\frac{3}{2}$
• B. $\frac{7}{2}$
• C. $\frac{5}{3}$
• D. $\frac{9}{7}$

Answer 1

The correct option is A $\frac{3}{2}$

$P{T}^{\frac{\gamma }{1-\gamma }}=$ Constant for reversible adiabatic process

$P{T}^{-3}=$ Constant

$\frac{\gamma }{1-\gamma }=-3$

$\gamma =-3+3\gamma$; $3=2y$ so $\gamma =3/2$.