Certainly! Let's walk through the steps needed to determine the amount of heat absorbed by a 35.64 g sample of iron when it is heated from 25 °C to 78 °C.
### Step 1: Understanding the Problem
We are given:
- The specific heat capacity of iron: [tex]\( c = 0.450 \, \text{J/g}^\circ\text{C} \)[/tex]
- The mass of the iron sample: [tex]\( m = 35.64 \, \text{g} \)[/tex]
- The initial temperature ([tex]\( T_{\text{initial}} \)[/tex]): [tex]\( 25 \, ^\circ\text{C} \)[/tex]
- The final temperature ([tex]\( T_{\text{final}} \)[/tex]): [tex]\( 78 \, ^\circ\text{C} \)[/tex]
We need to calculate the heat absorbed ([tex]\( Q \)[/tex]).
### Step 2: Calculate the Temperature Change
First, determine the change in temperature ([tex]\( \Delta T \)[/tex]):
[tex]\[ \Delta T = T_{\text{final}} - T_{\text{initial}} \][/tex]
[tex]\[ \Delta T = 78 \, ^\circ\text{C} - 25 \, ^\circ\text{C} \][/tex]
[tex]\[ \Delta T = 53 \, ^\circ\text{C} \][/tex]
### Step 3: Apply the Specific Heat Formula
The formula to calculate heat absorbed is:
[tex]\[ Q = mc\Delta T \][/tex]
where:
- [tex]\( Q \)[/tex] is the heat absorbed
- [tex]\( m \)[/tex] is the mass
- [tex]\( c \)[/tex] is the specific heat capacity
- [tex]\( \Delta T \)[/tex] is the temperature change
### Step 4: Plug in the Values
Substitute the values into the formula:
[tex]\[ Q = 35.64 \, \text{g} \times 0.450 \, \text{J/g}^\circ\text{C} \times 53 \, ^\circ\text{C} \][/tex]
### Step 5: Perform the Multiplication
Let's calculate:
[tex]\[ Q = 35.64 \times 0.450 \times 53 \][/tex]
[tex]\[ Q = 35.64 \times 23.85 \][/tex]
[tex]\[ Q = 850.014 \, \text{J} \][/tex]
### Summary
The temperature change for the iron sample is [tex]\( 53 \, ^\circ\text{C} \)[/tex]. The amount of heat absorbed by the 35.64 g sample of iron when it is heated from 25 °C to 78 °C is [tex]\( 850.014 \, \text{J} \)[/tex].
Thus, the results are:
- Temperature change ([tex]\( \Delta T \)[/tex]): [tex]\( 53 \, ^\circ\text{C} \)[/tex]
- Heat absorbed ([tex]\( Q \)[/tex]): [tex]\( 850.014 \, \text{J} \)[/tex]
