To find the amount of heat energy required to raise the temperature of 5 kg of paraffin by [tex]\(10^{\circ} \text{C}\)[/tex], we will follow a step-by-step process.
### Step 1: Find the Specific Heat Capacity
We start with the information given:
- [tex]\(1 \, \text{kg}\)[/tex] of paraffin requires [tex]\(44000 \, \text{J}\)[/tex] to raise its temperature by [tex]\(20^{\circ} \text{C}\)[/tex].
The formula for specific heat capacity ([tex]\(c\)[/tex]) is:
[tex]\[ c = \frac{Q}{m \Delta T} \][/tex]
where:
- [tex]\(Q\)[/tex] is the heat energy supplied,
- [tex]\(m\)[/tex] is the mass of the substance,
- [tex]\(\Delta T\)[/tex] is the change in temperature.
Plugging in the given values:
[tex]\[ c = \frac{44000 \, \text{J}}{1 \, \text{kg} \times 20^{\circ} \text{C}} \][/tex]
So,
[tex]\[ c = \frac{44000}{20} \, \text{J/(kg} \, ^{\circ} \text{C)} \][/tex]
This simplifies to:
[tex]\[ c = 2200 \, \text{J/(kg} \, ^{\circ} \text{C)} \][/tex]
### Step 2: Calculate the Heat Required for the Given Mass and Temperature Change
Now, we need to calculate the heat required to raise the temperature of 5 kg of paraffin by [tex]\(10^{\circ} \text{C}\)[/tex].
We use the formula:
[tex]\[ Q = mc \Delta T \][/tex]
Where:
- [tex]\(m = 5 \, \text{kg}\)[/tex],
- [tex]\(c = 2200 \, \text{J/(kg} \, ^{\circ} \text{C)}\)[/tex],
- [tex]\(\Delta T = 10^{\circ} \text{C}\)[/tex].
Plugging in the values:
[tex]\[ Q = 5 \, \text{kg} \times 2200 \, \text{J/(kg} \, ^{\circ} \text{C)} \times 10^{\circ} \text{C} \][/tex]
Calculating the product:
[tex]\[ Q = 5 \times 2200 \times 10 \, \text{J} \][/tex]
[tex]\[ Q = 110000 \, \text{J} \][/tex]
Thus, the amount of heat energy required to raise the temperature of 5 kg of paraffin by [tex]\(10^{\circ} \text{C}\)[/tex] is [tex]\(110000 \, \text{J}\)[/tex].
### Final Answer
The heat energy required is [tex]\(1.1 \times 10^5 \, \text{J}\)[/tex].
