Question

The pressure P of an ideal of gas in p is given by the equation P=1/3pC^2) where <C^2> is the mean squared speed and its measured as [speed]^2. Use the base units to show that the equation is homogeneous.

Answer 1

Answer on Question #74978-Physics-Mechanics-Relativity

The pressure $P$ of an ideal of gas in $p$ is given by the equation $P = 1 / 3pC^{\wedge}2$ where $< C^{\wedge}2 >$ is the mean squared speed and its measured as [speed] $\hat{\mathbf{\Gamma}}^2$ . Use the base units to show that the equation is homogeneous.

Solution

$$[ P ] = \frac {N}{m ^ {2}} = \frac {k g \frac {m}{s ^ {2}}}{m ^ {2}} = k g m ^ {- 1} s ^ {- 2}.$$ $$\left[ \frac {1}{3} \rho C ^ {2} \right] = \left[ \frac {1}{3} \right] [ \rho ] [ C ^ {2} ] = 1 \left(\frac {k g}{m ^ {3}}\right) \left(\frac {m ^ {2}}{s ^ {2}}\right) = k g m ^ {- 1} s ^ {- 2}$$

Thus,

$$[ P ] = \left[ \frac {1}{3} \rho C ^ {2} \right]$$

So, the equation is homogeneous.

Answer provided by https://www.AssignmentExpert.com