Question

how much heat is needed to melt 20.50 kg of silver that is initially at 15 ∘c ? the melting point of silver is 961 ∘c , the heat of fusion is 88 kj/kg , the specific heat is 230 j/kg⋅c∘ .

Answer 1

To find the total heat required to melt 20.50 kg of silver starting at 15 °C, one must calculate the silver's heating to its melting point and the heat of fusion. The first step involves specific heat, and the second step uses the heat of fusion, which together provide the total heat required.

Step-by-step explanation:

Calculating the Heat Required to Melt Silver

To calculate the amount of heat needed to melt 20.50 kg of silver initially at 15 °C, two steps are required. First, we must calculate the heat needed to raise the temperature of silver from 15 °C to its melting point, 961 °C. We use the formula Q = mcΔT, where Q is the heat added, m is the mass, c is the specific heat, and ΔT is the change in temperature. Next, we use the heat of fusion to find the heat required to actually melt the silver once it's reached its melting point using Q = mLf, where Lf is the latent heat of fusion. Adding both quantities of heat together gives the total heat required.

First Step: Heating to Melting Point

Q1 = m * c * ΔT

Q1 = 20.50 kg * 230 J/kg°C * (961 °C - 15 °C)

Q1 = 20.50 kg * 230 J/kg°C * 946 °C

Second Step: Melting the Silver

Q2 = m * Lf

Q2 = 20.50 kg * 88 kJ/kg
Q2 = 20.50 kg * 88000 J/kg

Total heat (Q_total) required is the sum of Q1 and Q2.

The total heat required to melt 20.50 kg of silver initially at 15 °C, after raising it to the melting point, is the sum of the heat needed to raise its temperature to the melting point plus the heat needed for the actual phase change from solid to liquid.

Answer 2

The total heat required to melt 20.50 kg of silver, initially at 15 °C, is calculated by first raising the temperature of the silver to its melting point and then melting it, which results in a total heat requirement of 6276.17 kJ.

Step-by-step explanation:

To calculate the amount of heat required to melt 20.50 kg of silver, we'll first need to raise its temperature from 15 °C to its melting point at 961 °C using its specific heat capacity, and then melt it using the heat of fusion. The heat needed to raise the temperature, Q1, is calculated using the formula Q1 = m * c * ΔT, where m is the mass of the silver, c is the specific heat, and ΔT is the change in temperature. And to calculate the heat needed to melt the silver, Q2, use the formula Q2 = m * Lf, where Lf is the latent heat of fusion.

Firstly, to raise the silver to its melting point:

Mass of silver, m = 20.50 kg

Initial temperature, T1 = 15 °C

Final temperature (melting point), T2 = 961 °C

Specific heat of silver, c = 230 J/kg°C

ΔT (change in temperature) = T2 - T1 = 961 °C - 15 °C = 946 °C

Q1 = 20.50 kg * 230 J/kg°C * 946 °C = 4,472,170 J or 4472.17 kJ

Secondly, to melt the silver:

Latent heat of fusion of silver, Lf = 88 kJ/kg

Q2 = 20.50 kg * 88 kJ/kg = 1,804 kJ

Therefore, the total heat required to melt 20.50 kg of silver equals the sum of Q1 and Q2: 4472.17 kJ + 1804 kJ = 6276.17 kJ.