What is the change in entropy of the lead when 2.0 kg of molten lead at its melting point temperature solidifies? For lead: L V = 207 kcal/kg at 1744°C, L F = 5.9 kcal/kg at 328°C.
Express your answer using two significant figures in kcal/K
vuyikb
To calculate the change in entropy of the lead when it solidifies, we need to use the information given about the latent heat of fusion (L_F) and the latent heat of vaporization (L_V) of lead, as well as the temperature at which the phase change occurs.
First, let's calculate the heat released when the lead solidifies. This can be done using the formula:
Q = m * L_F
where Q is the heat released, m is the mass of lead, and L_F is the latent heat of fusion.
Given:
Mass of lead (m) = 2.0 kg
Latent heat of fusion of lead (L_F) = 5.9 kcal/kg
Plugging in the given values into the formula, we get:
Q = 2.0 kg * 5.9 kcal/kg = 11.8 kcal
Next, let's calculate the change in temperature during the phase change. This can be done using the formula:
ΔT = (T_f - T_i)
where ΔT is the change in temperature, T_f is the final temperature (melting point temperature), and T_i is the initial temperature (melting point temperature - 328°C).
Given:
Final temperature (T_f) = 328°C
Initial temperature (T_i) = 1744°C - 328°C = 1416°C
Plugging in the given values into the formula, we get:
ΔT = 328°C - 1416°C = -1088°C
Now, let's calculate the change in entropy. The change in entropy (ΔS) can be calculated using the formula:
ΔS = Q / ΔT
Given:
Q = 11.8 kcal
ΔT = -1088°C
First, let's convert the change in temperature from Celsius to Kelvin. This can be done by adding 273 to the temperature in Celsius:
ΔT = -1088°C + 273 = -815 K
Plugging in the given values into the formula, we get:
ΔS = 11.8 kcal / -815 K = -0.014 kcal/K
To express the answer with two significant figures, we round the final value to -0.01 kcal/K.
Therefore, the change in entropy of the lead when 2.0 kg of molten lead at its melting point temperature solidifies is -0.01 kcal/K.