Question

How does Magic numberof nucleons confer stability to some atomic nuclides?
Explain with one suitable nuclear model.

Answer 1

Answer on Question #76843, Physics / Molecular Physics | Thermodynamics

A block of copper of mass 980g at a temperature of 120 degrees Celsius was placed in a beaker if water containing 250cm3 of water. If the water is at 12 degrees Celsius, explain what happens to the water with calculation for evidence.

Shc of water= 4200 J kg-1 K-1 Latent heat of fusion (Lf) = 2,340,000 J kg-1 shc of copper = 450 J kg-1 K-1

Solution

Firstly let's consider an ideal situation when a block of copper is placed in a beaker and there is no exchange of matter and heat with surrounding. Then we will consider a real situation.

When a block of copper at temperature $120^{\circ}\mathrm{C}$ is placed in a beaker with water at temperature $12^{\circ}\mathrm{C}$ a process of heat exchange takes place until the temperature of heat equilibrium is reached.

A block of copper releases heat $Q_{\text{released}}$. Water absorbs heat $Q_{\text{absorbed}}$.

At the state of heat equilibrium $Q_{\text{released}} = Q_{\text{absorbed}}$,

$$Q_{\text{released}} = \mathrm{cm} (T_2 - T_1)$$

Where $c(\mathrm{Cu}) = 450 \, \mathrm{J/kg \cdot K}$

$$m(\mathrm{Cu}) = 0.980 \, \mathrm{kg}$$ $$T_1 = 120 + 273.15 = 393.15 \, \mathrm{K}$$ $$Q_{\text{released}} = 450 \cdot 0.980 (T_2 - 393.15)$$ $$Q_{\text{absorbed}} = \mathrm{cm} (T_2 - T_1)$$ $$c(\mathrm{H_2O}) = 4200 \, \mathrm{J/kg \cdot K}$$ $$m(\mathrm{H_2O}) = V(\mathrm{H_2O}) \cdot d(\mathrm{H_2O}), \, d(\mathrm{H_2O}) = 1 \, \mathrm{g/cm^3};$$ $$m(\mathrm{H_2O}) = 250 \cdot 1 = 250 \, (\mathrm{g}) = 0.250 \, \mathrm{kg}$$ $$T_1 = 12 + 273.15 = 285.15 \, \mathrm{K}$$ $$Q_1 = 4200 \cdot 0.250 (T_2 - 285.15)$$ $$Q_{\text{released}} = Q_{\text{absorbed}};$$ $$-450 \cdot 0.980 (T_2 - 393.15) = 4200 \cdot 0.250 (T_2 - 285.15)$$ T_2 = 317.09 \, \mathrm{K} \text{ or } T_2 = 317.09 - 273.15 = 43.94 \, ^\circ\mathrm{C}.

In real situation the heat will also be absorbed by beaker. And there also will the heat exchange with surrounding.

Observation: the water will be heated to the temperature of $43.94^{\circ}\mathrm{C}$, the block of copper will be cooled to the temperature of $43.94^{\circ}\mathrm{C}$.

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