Question
The specific heat for iron 0.450 J/g times K. A piece of iron increases from 27.2 degrees C to 31.4 degrees C when of energy is added to it. What is the mass of the iron?
A. 1.65 x 10^-4 g
B. 343 g
C. 0.0029 g
D. 286 g
A. 1.65 x 10^-4 g
B. 343 g
C. 0.0029 g
D. 286 g
Answers
GPT-4o mini
To find the mass of the iron, we can use the equation for heat transfer:
\[
q = m \cdot c \cdot \Delta T
\]
Where:
- \( q \) = heat added (in joules)
- \( m \) = mass (in grams)
- \( c \) = specific heat capacity (in J/g·K)
- \( \Delta T \) = change in temperature (in °C or K)
**Given:**
- Specific heat capacity of iron, \( c = 0.450 \, \text{J/g·K} \)
- Initial temperature, \( T_i = 27.2 \, °C \)
- Final temperature, \( T_f = 31.4 \, °C \)
**Calculating the change in temperature (\( \Delta T \))**:
\[
\Delta T = T_f - T_i = 31.4 \, °C - 27.2 \, °C = 4.2 \, °C
\]
Now we can rearrange the heat transfer equation to solve for the mass \( m \):
\[
m = \frac{q}{c \cdot \Delta T}
\]
Since the amount of energy \( q \) is not provided in your question, let’s assume a hypothetical amount of energy (you'll need the actual value for a final answer). Let's denote the energy added as \( q \).
Substituting the values into the equation, we get:
\[
m = \frac{q}{0.450 \, \text{J/g·K} \cdot 4.2 \, \text{K}} = \frac{q}{1.89 \, \text{J/g}}
\]
In order to get the exact mass, please provide the value for \( q \).
If \( q \) is known, just plug that value into the equation to find the mass of iron. If you have options A, B, C, or D that relate to a specific value of \( q \), use those to match the calculated mass.
If we were assuming a value of \( q \) (not provided in your statement), we cannot decide from the given options alone without that specific energy amount. Can you please confirm the energy \( q \) added?
\[
q = m \cdot c \cdot \Delta T
\]
Where:
- \( q \) = heat added (in joules)
- \( m \) = mass (in grams)
- \( c \) = specific heat capacity (in J/g·K)
- \( \Delta T \) = change in temperature (in °C or K)
**Given:**
- Specific heat capacity of iron, \( c = 0.450 \, \text{J/g·K} \)
- Initial temperature, \( T_i = 27.2 \, °C \)
- Final temperature, \( T_f = 31.4 \, °C \)
**Calculating the change in temperature (\( \Delta T \))**:
\[
\Delta T = T_f - T_i = 31.4 \, °C - 27.2 \, °C = 4.2 \, °C
\]
Now we can rearrange the heat transfer equation to solve for the mass \( m \):
\[
m = \frac{q}{c \cdot \Delta T}
\]
Since the amount of energy \( q \) is not provided in your question, let’s assume a hypothetical amount of energy (you'll need the actual value for a final answer). Let's denote the energy added as \( q \).
Substituting the values into the equation, we get:
\[
m = \frac{q}{0.450 \, \text{J/g·K} \cdot 4.2 \, \text{K}} = \frac{q}{1.89 \, \text{J/g}}
\]
In order to get the exact mass, please provide the value for \( q \).
If \( q \) is known, just plug that value into the equation to find the mass of iron. If you have options A, B, C, or D that relate to a specific value of \( q \), use those to match the calculated mass.
If we were assuming a value of \( q \) (not provided in your statement), we cannot decide from the given options alone without that specific energy amount. Can you please confirm the energy \( q \) added?