Question
The specific heat for iron is 0.450 J/g⋅K . A piece of iron increases from 27.2°C to 31.4°C when of energy is added to it. What is the mass of the iron?(1 point) Responses 286 g 286 g 0.0029 g 0 point 0 0 2 9 g 1.65×10−4 g 1 point 6 5 times 10 to the negative 4 power g 343 g
Answers
GPT-4o mini
To determine the mass of the iron piece based on the given information, we can use the formula for heat transfer:
\[
q = m \cdot c \cdot \Delta T
\]
where:
- \( q \) is the heat added (in Joules),
- \( m \) is the mass (in grams),
- \( c \) is the specific heat capacity (in J/g⋅K), and
- \( \Delta T \) is the change in temperature (in K or °C).
Given:
- The specific heat capacity of iron, \( c = 0.450 \, \text{J/g⋅K} \),
- Initial temperature \( T_i = 27.2 \, \text{°C} \),
- Final temperature \( T_f = 31.4 \, \text{°C} \).
First, we need to calculate the change in temperature:
\[
\Delta T = T_f - T_i = 31.4 \, \text{°C} - 27.2 \, \text{°C} = 4.2 \, \text{°C} = 4.2 \, \text{K}
\]
Since we do not have the heat \( q \) given in the problem, let's assume you meant to provide a specific value for \( q \).
**Assuming \( q \) = 100 J for calculation:**
Now substituting the values into the heat transfer equation:
\[
100 = m \cdot 0.450 \cdot 4.2
\]
To find the mass \( m \):
\[
m = \frac{100}{0.450 \cdot 4.2}
\]
Calculate \( 0.450 \cdot 4.2 \):
\[
0.450 \cdot 4.2 = 1.89
\]
Now substitute this back into the equation for \( m \):
\[
m = \frac{100}{1.89} \approx 52.9 \, \text{g}
\]
Since \( q \) was needed as input for the final calculation and wasn't given in your message, please provide the amount of energy \( q \) added to the iron piece in order to correctly calculate its mass.
If you have a specific value for \( q \), I can substitute that in and compute the mass for you.
\[
q = m \cdot c \cdot \Delta T
\]
where:
- \( q \) is the heat added (in Joules),
- \( m \) is the mass (in grams),
- \( c \) is the specific heat capacity (in J/g⋅K), and
- \( \Delta T \) is the change in temperature (in K or °C).
Given:
- The specific heat capacity of iron, \( c = 0.450 \, \text{J/g⋅K} \),
- Initial temperature \( T_i = 27.2 \, \text{°C} \),
- Final temperature \( T_f = 31.4 \, \text{°C} \).
First, we need to calculate the change in temperature:
\[
\Delta T = T_f - T_i = 31.4 \, \text{°C} - 27.2 \, \text{°C} = 4.2 \, \text{°C} = 4.2 \, \text{K}
\]
Since we do not have the heat \( q \) given in the problem, let's assume you meant to provide a specific value for \( q \).
**Assuming \( q \) = 100 J for calculation:**
Now substituting the values into the heat transfer equation:
\[
100 = m \cdot 0.450 \cdot 4.2
\]
To find the mass \( m \):
\[
m = \frac{100}{0.450 \cdot 4.2}
\]
Calculate \( 0.450 \cdot 4.2 \):
\[
0.450 \cdot 4.2 = 1.89
\]
Now substitute this back into the equation for \( m \):
\[
m = \frac{100}{1.89} \approx 52.9 \, \text{g}
\]
Since \( q \) was needed as input for the final calculation and wasn't given in your message, please provide the amount of energy \( q \) added to the iron piece in order to correctly calculate its mass.
If you have a specific value for \( q \), I can substitute that in and compute the mass for you.