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 1.65×10−4 g 1 point 6 5 times 10 to the negative 4 power g 286 g 286 g 0.0029 g 0 point 0 0 2 9 g 343 g
Answers
GPT-4o mini
To find the mass of the iron, we can use the formula for heat transfer:
\[
Q = mc\Delta T
\]
where:
- \( Q \) is the heat energy 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 Kelvin or °C).
From the problem:
- The specific heat \( c = 0.450 \, \text{J/g⋅K} \)
- The initial temperature \( T_i = 27.2 \, °C \)
- The final temperature \( T_f = 31.4 \, °C \)
- The change in temperature \( \Delta T = T_f - T_i = 31.4°C - 27.2°C = 4.2°C \)
Now, we need to express \( Q \) to find the mass \( m \). Since \( Q \) is not provided, we can express it in terms of \( m \) based on the formula:
\[
Q = mc\Delta T
\]
Plugging in the known values:
\[
Q = m \cdot 0.450 \, \text{J/g⋅K} \cdot 4.2 \, \text{K}
\]
We need to determine which answer corresponds to meaningful mass under an assumption of a specific amount of heat energy added \( Q \). However, we need more information about \( Q \) to solve for \( m \) directly.
If we assume \( Q \) is given or can be rearranged directly around a deduced value or certain logical energies (like a typical heat energy measurement), we can compute, but in this scenario, another piece of information or the context for \( Q \) would be essential.
For example, if you know that \( Q \) equals x joules, you could then find the mass \( m \):
\[
m = \frac{Q}{c \Delta T}
\]
Without the amount of energy \( Q \) provided in the question, we cannot determine the mass with the information given. If you can clarify or provide the amount of energy added to the iron, we can proceed with the calculation.
However, given the responses, if any assumed specific total energy Q values were to be intelligently speculated or approximated, it could lead to recognizing mass responses from ans largely indicated around typical heat energy ranges:
- 286 g appears as a considerably more feasible mass related toward iron than others shown.
Could you please provide \( Q \) in this context, or clarify if any energy values need to be evaluated for deduction?
\[
Q = mc\Delta T
\]
where:
- \( Q \) is the heat energy 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 Kelvin or °C).
From the problem:
- The specific heat \( c = 0.450 \, \text{J/g⋅K} \)
- The initial temperature \( T_i = 27.2 \, °C \)
- The final temperature \( T_f = 31.4 \, °C \)
- The change in temperature \( \Delta T = T_f - T_i = 31.4°C - 27.2°C = 4.2°C \)
Now, we need to express \( Q \) to find the mass \( m \). Since \( Q \) is not provided, we can express it in terms of \( m \) based on the formula:
\[
Q = mc\Delta T
\]
Plugging in the known values:
\[
Q = m \cdot 0.450 \, \text{J/g⋅K} \cdot 4.2 \, \text{K}
\]
We need to determine which answer corresponds to meaningful mass under an assumption of a specific amount of heat energy added \( Q \). However, we need more information about \( Q \) to solve for \( m \) directly.
If we assume \( Q \) is given or can be rearranged directly around a deduced value or certain logical energies (like a typical heat energy measurement), we can compute, but in this scenario, another piece of information or the context for \( Q \) would be essential.
For example, if you know that \( Q \) equals x joules, you could then find the mass \( m \):
\[
m = \frac{Q}{c \Delta T}
\]
Without the amount of energy \( Q \) provided in the question, we cannot determine the mass with the information given. If you can clarify or provide the amount of energy added to the iron, we can proceed with the calculation.
However, given the responses, if any assumed specific total energy Q values were to be intelligently speculated or approximated, it could lead to recognizing mass responses from ans largely indicated around typical heat energy ranges:
- 286 g appears as a considerably more feasible mass related toward iron than others shown.
Could you please provide \( Q \) in this context, or clarify if any energy values need to be evaluated for deduction?