Math Problem Statement

The average speed of a gas molecule in meters per second is v avg = root(8RT/piM), where the temperature T is given in kelvins, the molar mass M is given in kilogram--moles, and R = 8.31. Calculate dv avg / dT at T=350 K for oxygen, which has a molar mass of 0.032 kg/mol. Use decimal notation, give your answer to four decimal places.

d/dT v avg = ? m/(s⋅K)

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Physics (Thermodynamics)

Formulas

v_avg = √(8RT / πM)
d(v_avg) / dT = (1/2) * (8R / πM)^(1/2) * T^(-1/2)

Theorems

Power Rule for Differentiation

Suitable Grade Level

Undergraduate (Calculus and Thermodynamics)