calculate the quantity of heat required to raise the temperature of 1g of ice from -10c to 110c
To calculate the quantity of heat required to raise the temperature of a substance, we need to use the specific heat capacity formula.
The specific heat capacity (c) is the amount of heat required to raise the temperature of a substance per unit mass. For ice, its specific heat capacity is approximately 2.09 J/g°C.
We need to break the calculation into two parts:
1. Calculating the heat required to raise the temperature of ice from -10°C to 0°C
2. Calculating the heat required to raise the temperature of water from 0°C to 110°C
Let's begin:
1. Calculating the heat required to raise the temperature of ice from -10°C to 0°C:
First, we need to raise the temperature of 1 gram of ice from -10°C to 0°C. The temperature change (ΔT) is 0°C - (-10°C) = 10°C.
The heat required (Q) is calculated using the formula: Q = m * c * ΔT
where
- Q is the heat required
- m is the mass of the substance (1g in this case)
- c is the specific heat capacity of the substance (2.09 J/g°C)
- ΔT is the change in temperature (10°C)
Substituting the values into the formula, we get: Q = 1g * 2.09 J/g°C * 10°C = 20.9 J
Therefore, the heat required to raise the temperature of 1g of ice from -10°C to 0°C is 20.9 Joules.
2. Calculating the heat required to raise the temperature of water from 0°C to 110°C:
After reaching 0°C, the ice will continue to heat up until it reaches its melting point. At this point, it will start to melt into water. The specific heat capacity of water (c) is approximately 4.18 J/g°C.
The temperature change (ΔT) from 0°C to 100°C is 100°C - 0°C = 100°C.
The heat required (Q) is calculated using the formula: Q = m * c * ΔT
where
- Q is the heat required
- m is the mass of the substance (1g in this case)
- c is the specific heat capacity of water (4.18 J/g°C)
- ΔT is the change in temperature (100°C)
Substituting the values into the formula, we get: Q = 1g * 4.18 J/g°C * 100°C = 418 J
Therefore, the heat required to raise the temperature of 1g of water from 0°C to 100°C is 418 Joules.
Finally, to calculate the total heat required, we add the two calculated values together:
Total heat = Heat required to raise ice temperature + Heat required to raise water temperature
Total heat = 20.9 J + 418 J = 438.9 J
Therefore, the quantity of heat required to raise the temperature of 1g of ice from -10°C to 110°C is approximately 438.9 Joules.