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II. Heterogeneous Nucleation: YSL VLM Y SM R The surface area and volume of a spherical cap of radius R and contact angle 0, on a flat surface = πρ are given by Ast = 2πR² (1- cos) and VS. -(2+ cos 0) (1- cos 0)², respectively. The SL 3 contact area with the flat surface is ASM = πR² sin² 0. a) Show that the critical nucleus radius R* is independent of the contact angle 0, and express R* in terms of the ratio of Ah, /YSL, the melting point Tm, and the temperature T. ν b) Graph the ratio of activation energy for heterogeneous nucleation (0≤0<π) to that for homogeneous nucleation (0 = π ) as a function of contact angle; i.e., your y-axis value should be 1 at 0 =π and less than 1 everywhere else.

II. Heterogeneous Nucleation: YSL VLM Y SM R The surface area and volume of a spherical cap of radius R and contact angle 0, on a flat surface = πρ are given by Ast = 2πR² (1- cos) and VS. -(2+ cos 0) (1- cos 0)², respectively. The SL 3 contact area with the flat surface is ASM = πR² sin² 0. a) Show that the critical nucleus radius R* is independent of the contact angle 0, and express R* in terms of the ratio of Ah, /YSL, the melting point Tm, and the temperature T. ν b) Graph the ratio of activation energy for heterogeneous nucleation (0≤0<π) to that for homogeneous nucleation (0 = π ) as a function of contact angle; i.e., your y-axis value should be 1 at 0 =π and less than 1 everywhere else.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter1: Basic Modes Of Heat Transfer
Section: Chapter Questions
Problem 1.55P
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II. Heterogeneous Nucleation: YSL VLM Y SM R The surface area and volume of a spherical cap of radius R and contact angle 0, on a flat surface = πρ are given by Ast = 2πR² (1- cos) and VS. -(2+ cos 0) (1- cos 0)², respectively. The SL 3 contact area with the flat surface is ASM = πR² sin² 0. a) Show that the critical nucleus radius R* is independent of the contact angle 0, and express R* in terms of the ratio of Ah, /YSL, the melting point Tm, and the temperature T. ν b) Graph the ratio of activation energy for heterogeneous nucleation (0≤0<π) to that for homogeneous nucleation (0 = π ) as a function of contact angle; i.e., your y-axis value should be 1 at 0 =π and less than 1 everywhere else.
Transcribed Image Text:II. Heterogeneous Nucleation: YSL VLM Y SM R The surface area and volume of a spherical cap of radius R and contact angle 0, on a flat surface = πρ are given by Ast = 2πR² (1- cos) and VS. -(2+ cos 0) (1- cos 0)², respectively. The SL 3 contact area with the flat surface is ASM = πR² sin² 0. a) Show that the critical nucleus radius R* is independent of the contact angle 0, and express R* in terms of the ratio of Ah, /YSL, the melting point Tm, and the temperature T. ν b) Graph the ratio of activation energy for heterogeneous nucleation (0≤0<π) to that for homogeneous nucleation (0 = π ) as a function of contact angle; i.e., your y-axis value should be 1 at 0 =π and less than 1 everywhere else.
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