Question

The speed of sound in a gas is given by $v=\sqrt{\frac{\gamma RT}{M}}$
$R=$ universal gas constant,
$T=$ temperature
$M=$ molar mass of gas
The dimensional formula of $\gamma$ is

• A. $\left[M^0{L}^0{T}^0\right]$
• B. $\left[M^{0}L{T}^{-1}\right]$
• C. $\left[ML{T}^{-2}\right]$
• D. $\left[M^0{L}^0{T}^{-1}\right]$

Answer 1

Answer: (A)

$\left[M^0{L}^0{T}^0\right]$

$\gamma$ is the ratio of specific heat at constant pressure to the specific heat at constant volume.Hence it is the ratio of like quantities, therefore dimensionless.