Question

Which of the following equations represent the solubility (S) of the hydrogen in the metals?

(a) S = C exp[-Es/(kθ)]

(b) S = C exp[-Es*(kθ)]

(c) S = C log[-Es/(kθ)]

(d) S = C log[-Es*(kθ)]

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Asked question is from Gases in Metals in section Pouring – Gating Design, Melting Furnaces, Melting and Casting Quality of Casting-Forming-Welding I

Answer 1

The correct answer is:

(a) S = C exp[-Es/(kθ)]

Explanation:

The solubility of hydrogen in metals is often modeled using an equation similar to the Arrhenius equation, which describes how solubility (S) changes with temperature. In this case, the solubility of hydrogen in metals can be represented as:

S=Cexp⁡(−Eskθ)S = C \exp\left(-\frac{E_s}{k \theta}\right)S=Cexp(−kθEs​​)

Where:

• S is the solubility of hydrogen in the metal.
• C is a constant.
• E_s is the enthalpy of solution of hydrogen in the metal.
• k is the Boltzmann constant.
• θ is the temperature (in appropriate units, such as Kelvin).

The exponential term exp⁡(−Eskθ)\exp\left(-\frac{E_s}{k \theta}\right)exp(−kθEs​​) indicates that the solubility decreases as the temperature increases, as expected for gases dissolving in metals.

Thus, (a) S = C exp[-Es/(kθ)] correctly represents the relationship between solubility and temperature in this context.

The other options involving logarithms are incorrect, as the solubility of gases in metals is typically described by an exponential function, not a logarithmic one.