Questions: Solve the following equation for "T" using the values of the other variables listed below. Express your answer as a decimal number with at least four digits past the decimal. u = sqrt((3 * R * T) / M) u = 402 M = 0.048 R = 8.314

Solution Steps

Given the equation: \[ u = \sqrt{\frac{3 \cdot R \cdot T}{M}} \]

Substitute the given values: \[ u = 402, \quad M = 0.048, \quad R = 8.314 \]

First, square both sides of the equation to eliminate the square root: \[ u^2 = \frac{3 \cdot R \cdot T}{M} \]

Next, solve for \( T \): \[ T = \frac{u^2 \cdot M}{3 \cdot R} \]

Substitute \( u = 402 \), \( M = 0.048 \), and \( R = 8.314 \) into the equation: \[ T = \frac{402^2 \cdot 0.048}{3 \cdot 8.314} \]

Calculate \( 402^2 \): \[ 402^2 = 161604 \]

Then, multiply by \( 0.048 \): \[ 161604 \cdot 0.048 = 7756.992 \]

Finally, divide by \( 3 \cdot 8.314 \): \[ 3 \cdot 8.314 = 24.942 \]

\[ T = \frac{7756.992}{24.942} \approx 310.9371 \]

Final Answer