Question

The hot working temperature of lead

• A. $300^\circ\text{C}$
• B. $100^\circ\text{C}$
• C. $200^\circ\text{C}$
• D. Room temperature

Hint:

Hot working does not necessarily mean "hot to touch."
It simply means working a metal above its recrystallization temperature.
Lead at room temperature is being hot worked, while iron at $400^\circ\text{C}$ is still being cold worked.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks for the temperature range at which the plastic deformation of lead (Pb) is classified as "hot working".

Step 2: Key Formula or Approach:
The dividing line between cold working and hot working is the recrystallization temperature ($T_{\text{recrys}}$):
\[ T_{\text{recrys}} \approx 0.4 \times T_m \quad (\text{in Kelvin}) \]
where $T_m$ is the absolute melting temperature of the metal.

Step 3: Detailed Explanation:

• Lead (Pb) is a soft metal with a very low melting point:
\[ T_m = 327^\circ\text{C} = 600\text{ K} \]

• Calculating the absolute recrystallization temperature of lead:
\[ T_{\text{recrys}} \approx 0.4 \times 600\text{ K} = 240\text{ K} = -33^\circ\text{C} \]

• Because the recrystallization temperature of lead is well below room temperature ($25^\circ\text{C} = 298\text{ K}$), any deformation performed at room temperature occurs above $T_{\text{recrys}}$.

• During deformation at room temperature, the grains of lead spontaneously recrystallize, continuously healing structural damage and preventing work hardening.

• Therefore, deforming lead at room temperature is thermodynamically classified as hot working.

Step 4: Final Answer:
The hot working temperature of lead is Room temperature.