Question

На монетном дворе отливают золотые слитки массой 1 кг. Сколько энергии передаёт такой слиток окружающей среде с момента начала кристаллизации до окончательного охлаждения? Температура в цеху 24 градусов.

Answer 1

Q1=лямбда*m=0,67*10^5*1= 0,67*10^5Дж    Q2=c*m*(tпл-t)=130*1*(1063-24)=135070Дж   Q1+Q2=202070Дж

Answer 2

Calculating Energy Transfer During Solidification of Gold Ingot

To calculate the energy transfer during the solidification of a gold ingot, we can use the formula for latent heat of fusion and the specific heat capacity of gold.

Given: - Mass of gold ingot, m = 1 kg - Initial temperature, T_initial = 1064°C (melting point of gold) - Final temperature, T_final = 24°C (temperature in the workshop)

Calculating Latent Heat of Fusion:

The energy required for the phase change from liquid to solid can be calculated using the formula: \[ Q = m \times L_f \] Where: - Q is the energy transferred - m is the mass of the substance - L_f is the latent heat of fusion

The latent heat of fusion for gold is approximately 64.9 kJ/mol [[1 #1]].

Using the molar mass of gold (197 g/mol), we can convert the latent heat of fusion to kJ/kg: \[ L_f = 64.9 \, kJ/mol \times \frac{1 \, kg}{0.197 \, kg/mol} \approx 330 \, kJ/kg \]

Substituting the values: \[ Q = 1 \, kg \times 330 \, kJ/kg = 330 \, kJ \]

Calculating Energy Transfer for Cooling:

The energy transferred during the cooling process can be calculated using the formula: \[ Q = m \times c \times \Delta T \] Where: - c is the specific heat capacity - ΔT is the change in temperature

The specific heat capacity of gold is approximately 0.129 J/g°C or 129 J/kg°C [[1 #1]].

Converting the specific heat capacity to kJ/kg°C: \[ c = 129 \, J/kg°C \times 10^{-3} = 0.129 \, kJ/kg°C \]

Substituting the values: \[ Q = 1 \, kg \times 0.129 \, kJ/kg°C \times (1064 - 24)°C = 1 \, kg \times 0.129 \, kJ/kg°C \times 1040°C \approx 134.16 \, kJ \]

Total Energy Transfer:

The total energy transfer during the solidification and cooling of the gold ingot is the sum of the energy for phase change and the energy for cooling: \[ Total \, Energy = 330 \, kJ + 134.16 \, kJ = 464.16 \, kJ \]

Therefore, the gold ingot transfers approximately 464.16 kJ of energy to the surrounding environment during the process of solidification and cooling.