A 0.200 kg block of ice at -15 degrees Celsius is placed into a pan on a stove, heated to a liquid, and then to vapour with a final temperature of 115 degrees Celsius. Calculate the total amount of heat required for this process.

To find the total amount of heat required for this process, we will break the process into three parts: heating the ice from -15°C to 0°C, melting the ice at 0°C, and heating the resulting water from 0°C to 115°C.

1. Heating the ice from -15°C to 0°C:
To calculate the heat required for this process, we'll use the formula Q = mcΔT, where Q is the heat, m is the mass of the ice, c is the specific heat of the ice, and ΔT is the change in temperature. The specific heat of ice is 2100 J/(kg·°C).

Q1 = (0.200 kg) * (2100 J/(kg·°C)) * (0 - -15°C)
Q1 = 0.200 * 2100 * 15
Q1 = 6300 J

2. Melting the ice at 0°C:
To melt the ice, we'll use the formula Q = mL, where L is the latent heat of fusion for ice. The latent heat of fusion for ice is 334,000 J/kg.

Q2 = (0.200 kg) * (334,000 J/kg)
Q2 = 66800 J

3. Heating the resulting water from 0°C to 115°C:
Now that the ice is melted, we'll use the equation Q = mcΔT once again, but this time using the specific heat of water, which is 4186 J/(kg·°C).

Q3 = (0.200 kg) * (4186 J/(kg·°C)) * (115 - 0°C)
Q3 = 0.200 * 4186 * 115
Q3 = 96394 J

Finally, to find the total amount of heat required, we add the heat from each step:

Total = Q1 + Q2 + Q3
Total = 6300 J + 66800 J + 96394 J
Total = 169494 J

The total amount of heat required for this process is 169,494 J.

To calculate the total amount of heat required for this process, we need to consider three steps: heating the ice from -15 degrees Celsius to 0 degrees Celsius, melting the ice at 0 degrees Celsius, and heating the resulting water from 0 degrees Celsius to 100 degrees Celsius.

Step 1: Heating the ice from -15 degrees Celsius to 0 degrees Celsius:
The specific heat capacity of ice is 2.09 J/g°C.
Since the mass of the ice is 0.200 kg, the total heat required to raise the temperature from -15 degrees Celsius to 0 degrees Celsius can be calculated using the formula:

Q = m * c * ΔT

Where:
Q is the heat required
m is the mass of the ice
c is the specific heat capacity of ice
ΔT is the change in temperature

Plugging in the values, we have:
Q1 = 0.200 kg * 2.09 J/g°C * (0 - (-15) °C)
Q1 = 0.200 kg * 2.09 J/g°C * 15 °C
Q1 = 6.27 J/g * 0.200 kg
Q1 = 1.254 J

Step 2: Melting the ice at 0 degrees Celsius:
The heat required to melt the ice can be calculated using the formula:

Q = m * Lf

Where:
Q is the heat required
m is the mass of the ice
Lf is the latent heat of fusion of ice, which is 334 J/g

Plugging in the values, we have:
Q2 = 0.200 kg * 334 J/g
Q2 = 66.8 J

Step 3: Heating the resulting water from 0 degrees Celsius to 100 degrees Celsius:
The specific heat capacity of water is 4.18 J/g°C.
Since the mass of the ice is now in the liquid form, the total heat required to raise the temperature from 0 degrees Celsius to 100 degrees Celsius can be calculated using the formula:

Q = m * c * ΔT

Plugging in the values, we have:
Q3 = 0.200 kg * 4.18 J/g°C * (100 - 0) °C
Q3 = 0.200 kg * 4.18 J/g°C * 100 °C
Q3 = 83.6 J/g * 0.200 kg
Q3 = 16.72 J

Finally, to calculate the total amount of heat required for the entire process, we add the values obtained in each step:

Total heat required = Q1 + Q2 + Q3
Total heat required = 1.254 J + 66.8 J + 16.72 J
Total heat required = 84.774 J

Therefore, the total amount of heat required for the process is approximately 84.774 J.

To calculate the total amount of heat required for this process, we need to consider three steps:

1. Heating the ice to its melting point (0 degrees Celsius)
2. Melting the ice into liquid water
3. Heating the water to its boiling point (100 degrees Celsius) and turning it into vapour

Let's break down each step and calculate the heat required:

Step 1: Heating the ice to its melting point
The heat required to raise the temperature of the ice from -15 degrees Celsius to 0 degrees Celsius can be calculated using the formula:

Q = m * c * ΔT

Where:
Q = Heat energy
m = Mass of the ice = 0.200 kg
c = Specific heat capacity of ice = 2,093 J/kg°C (given value)
ΔT = Change in temperature = (0 - (-15)) = 15°C

Q1 = 0.200 kg * 2,093 J/kg°C * 15°C
Q1 = 6,279 J

Step 2: Melting the ice into liquid water
The heat required to melt the ice can be calculated using the formula:

Q = m * L

Where:
Q = Heat energy
m = Mass of the ice = 0.200 kg
L = Latent heat of fusion of ice = 334,000 J/kg (given value)

Q2 = 0.200 kg * 334,000 J/kg
Q2 = 66,800 J

Step 3: Heating the water to its boiling point and turning it into vapour
The heat required to raise the temperature of the water from its melting point (0 degrees Celsius) to its boiling point (100 degrees Celsius) can be calculated using the formula:

Q = m * c * ΔT

Where:
Q = Heat energy
m = Mass of the liquid water = 0.200 kg
c = Specific heat capacity of water = 4,186 J/kg°C (given value)
ΔT = Change in temperature = (100 - 0) = 100°C

Q3 = 0.200 kg * 4,186 J/kg°C * 100°C
Q3 = 83,720 J

The total amount of heat required for this process is the sum of Q1, Q2, and Q3:

Total heat required = Q1 + Q2 + Q3
Total heat required = 6,279 J + 66,800 J + 83,720 J
Total heat required ≈ 156,799 J

Therefore, the total amount of heat required for this process is approximately 156,799 Joules.