Question
In order for the specific heat equation to work correctly, temperature must be measured in (1 point) Responses Kelvin Kelvin Celsius Celsius Fahrenheit Fahrenheit Question 2 The specific heat of iron is 0.452 J/g * C. How much heat is released when 950g of iron cools from 75 degrees Celsius to 25 degrees Celsius?(2 points) Responses 21,470 J 21,470 J 805,125 J 805,125 J 8.6 J 8.6 J 579.4 J 579.4 J Question 3 The specific heat of copper is 0.385 J/g*C. A piece of copper is heated from 22 degrees Celsius to 88 degrees Celsius. - 8,992 J of heat are released. What is the mass of the copper?(2 points) Responses 228,486 g 228,486 g 228,486 N 228,486 N 353.8 g 353.8 g 353.8N 353.8N Skip to navigation
Answers
GPT-4o mini
Here's how to solve the questions you've asked:
### Question 1:
In order for the specific heat equation to work correctly, temperature must be measured in **Celsius** or **Kelvin**. However, for the sake of specific heat calculations, it's more common to use degrees Celsius because specific heat is often defined based on the temperature change, which is the same in either scale (Celsius or Kelvin). The response is valid for both, but in many contexts, Celsius is preferred.
### Question 2:
To calculate the heat released when the iron cools, we use the specific heat formula:
\[ q = m \cdot c \cdot \Delta T \]
where:
- \( q \) = heat transferred (in Joules)
- \( m \) = mass (in grams)
- \( c \) = specific heat (in J/g°C)
- \( \Delta T \) = change in temperature (in °C)
Given:
- \( m = 950 \, \text{g} \)
- \( c = 0.452 \, \text{J/g°C} \)
- Initial temperature \( T_i = 75 \, \text{°C} \)
- Final temperature \( T_f = 25 \, \text{°C} \)
Calculate the change in temperature:
\[ \Delta T = T_f - T_i = 25 \, \text{°C} - 75 \, \text{°C} = -50 \, \text{°C} \]
Now plug the values into the formula:
\[ q = 950 \, \text{g} \cdot 0.452 \, \text{J/g°C} \cdot (-50 \, \text{°C}) \]
\[ q = 950 \cdot 0.452 \cdot (-50) \]
\[ q = 950 \cdot 0.452 \cdot -50 = -21,470 \, \text{J} \]
Since we are interested in heat released, we take the positive value:
**21,470 J**
### Question 3:
Using the specific heat formula again, but now we rearrange to solve for mass:
\[ q = m \cdot c \cdot \Delta T \Rightarrow m = \frac{q}{c \cdot \Delta T} \]
Given:
- \( q = -8,992 \, \text{J} \) (released, so we'll take the absolute value in calculations)
- \( c = 0.385 \, \text{J/g°C} \)
- Initial temperature \( T_i = 22 \, \text{°C} \)
- Final temperature \( T_f = 88 \, \text{°C} \)
Calculate the change in temperature:
\[ \Delta T = T_f - T_i = 88 \, \text{°C} - 22 \, \text{°C} = 66 \, \text{°C} \]
Plug in the values:
\[ m = \frac{8,992 \, \text{J}}{0.385 \, \text{J/g°C} \cdot 66 \, \text{°C}} \]
\[ m = \frac{8,992}{25.410} \]
\[ m \approx 353.8 \, \text{g} \]
Therefore, the mass of the copper is approximately **353.8 g**.
### Summary of Responses:
1. **Celsius**
2. **21,470 J**
3. **353.8 g**
### Question 1:
In order for the specific heat equation to work correctly, temperature must be measured in **Celsius** or **Kelvin**. However, for the sake of specific heat calculations, it's more common to use degrees Celsius because specific heat is often defined based on the temperature change, which is the same in either scale (Celsius or Kelvin). The response is valid for both, but in many contexts, Celsius is preferred.
### Question 2:
To calculate the heat released when the iron cools, we use the specific heat formula:
\[ q = m \cdot c \cdot \Delta T \]
where:
- \( q \) = heat transferred (in Joules)
- \( m \) = mass (in grams)
- \( c \) = specific heat (in J/g°C)
- \( \Delta T \) = change in temperature (in °C)
Given:
- \( m = 950 \, \text{g} \)
- \( c = 0.452 \, \text{J/g°C} \)
- Initial temperature \( T_i = 75 \, \text{°C} \)
- Final temperature \( T_f = 25 \, \text{°C} \)
Calculate the change in temperature:
\[ \Delta T = T_f - T_i = 25 \, \text{°C} - 75 \, \text{°C} = -50 \, \text{°C} \]
Now plug the values into the formula:
\[ q = 950 \, \text{g} \cdot 0.452 \, \text{J/g°C} \cdot (-50 \, \text{°C}) \]
\[ q = 950 \cdot 0.452 \cdot (-50) \]
\[ q = 950 \cdot 0.452 \cdot -50 = -21,470 \, \text{J} \]
Since we are interested in heat released, we take the positive value:
**21,470 J**
### Question 3:
Using the specific heat formula again, but now we rearrange to solve for mass:
\[ q = m \cdot c \cdot \Delta T \Rightarrow m = \frac{q}{c \cdot \Delta T} \]
Given:
- \( q = -8,992 \, \text{J} \) (released, so we'll take the absolute value in calculations)
- \( c = 0.385 \, \text{J/g°C} \)
- Initial temperature \( T_i = 22 \, \text{°C} \)
- Final temperature \( T_f = 88 \, \text{°C} \)
Calculate the change in temperature:
\[ \Delta T = T_f - T_i = 88 \, \text{°C} - 22 \, \text{°C} = 66 \, \text{°C} \]
Plug in the values:
\[ m = \frac{8,992 \, \text{J}}{0.385 \, \text{J/g°C} \cdot 66 \, \text{°C}} \]
\[ m = \frac{8,992}{25.410} \]
\[ m \approx 353.8 \, \text{g} \]
Therefore, the mass of the copper is approximately **353.8 g**.
### Summary of Responses:
1. **Celsius**
2. **21,470 J**
3. **353.8 g**