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
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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)
Related Recommendation
Comparison of Most Probable Speed and Root Mean Square Speed in Ideal Gases
Calculate the Average Speed of Nitrogen Gas (N2) at 445K
Maxwell-Boltzmann Distribution Integral: Evaluating Particle Speed in a Gas
Calculate the Average Speed of a Chlorine Molecule at -155°C
Deriving the Maximum Speed of a Car Using Calculus in the Interval 0 <= t <= 3π/2q