How much energy is required to raise the temperature of 3 kg of iron from [tex]$20^{\circ}$[/tex] C to [tex]$25^{\circ} C$[/tex]? Use the table below and this equation: [tex]Q=m c \Delta T$[/tex].
| Substance | Specific Heat Capacity ([tex]$J /( g \cdot{ }^{\circ} C )$[/tex] ) |
| :---------- | :---------------------------------------------------- |
| Liquid water | 4.186 |
| Ice | 2.11 |
| Air | 1.00 |
| Aluminum | 0.897 |
| Soil | 0.80 |
| Granite | 0.790 |
| Iron | 0.450 |
| Copper | 0.385 |
| Silver | 0.233 |
| Lead | 0.129 |
A. 13.50 J
B. 6750 J
C. 1350 J
D. 2.25 J
Answer (2)
Convert the mass of iron to grams: 3 kg = 3000 g .
Calculate the change in temperature: Δ T = 2 5 ∘ C − 2 0 ∘ C = 5 ∘ C .
Use the formula Q = m c Δ T to find the energy required.
Calculate the energy: Q = ( 3000 g ) × ( 0.450 g ⋅ ∘ C J ) × ( 5 ∘ C ) = 6750 J .
Explanation
Problem Analysis We are given the mass of iron, the initial and final temperatures, and the specific heat capacity of iron. We need to find the amount of energy required to raise the temperature of the iron.
Mass Conversion First, we need to convert the mass of iron from kilograms to grams since the specific heat capacity is given in terms of grams. We know that 1 kg = 1000 g, so 3 kg = 3 * 1000 = 3000 g.
Temperature Change Next, we calculate the change in temperature, which is the final temperature minus the initial temperature: Δ T = T f − T i = 2 5 ∘ C − 2 0 ∘ C = 5 ∘ C .
Energy Calculation Now, we can use the formula Q = m c Δ T to calculate the energy required. We have m = 3000 g, c = 0.450 \frac{J}{g \,^{\circ}C} , and Δ T = 5 ∘ C . Plugging these values into the formula, we get: Q = ( 3000 g ) × ( 0.450 g ⋅ ∘ C J ) × ( 5 ∘ C ) = 6750 J .
Final Answer Therefore, the energy required to raise the temperature of 3 kg of iron from 2 0 ∘ C to 2 5 ∘ C is 6750 J.
Examples
Imagine you're heating an iron skillet on the stove. This calculation helps you determine how much energy your stove needs to supply to heat the skillet to a desired temperature. Knowing this can help you estimate energy costs or compare the efficiency of different cooking methods. This principle is also crucial in industrial processes where materials need to be heated to specific temperatures for manufacturing or treatment.
The energy required to raise the temperature of 3 kg of iron from 20°C to 25°C is calculated using the formula Q = m c Δ T . After converting the mass to grams and finding the change in temperature, we find that Q = 6750 J. Therefore, the correct answer is B. 6750 J.
;
