Questions: Solve the following equation for "T" using the values of the other variables listed below. u = sqrt(3 * R * T / M̄) u = 300 M̄ = 0.056 R = 8.314

Solve for \( T \) in the given equation.

Rearrange the equation to solve for \( T \).

The given equation is:
\[ u = \sqrt{\frac{3 \cdot R \cdot T}{\bar{M}}} \]
To solve for \( T \), first square both sides to eliminate the square root:
\[ u^2 = \frac{3 \cdot R \cdot T}{\bar{M}} \]
Now, solve for \( T \) by multiplying both sides by \( \bar{M} \) and dividing by \( 3 \cdot R \):
\[ T = \frac{u^2 \cdot \bar{M}}{3 \cdot R} \]

Substitute the given values into the equation.

Substitute \( u = 300 \), \( \bar{M} = 0.056 \), and \( R = 8.314 \) into the equation:
\[ T = \frac{300^2 \cdot 0.056}{3 \cdot 8.314} \]
Calculate the value:
\[ T = \frac{90000 \cdot 0.056}{24.942} \]
\[ T = \frac{5040}{24.942} \]
\[ T \approx 202.1 \]

\(\boxed{T \approx 202.1}\)

\(\boxed{T \approx 202.1}\)