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
343 g
343 g
1.65×10−4 g
1 point 6 5 times 10 to the negative 4 power g
0.0029 g
. 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
343 g
343 g
1.65×10−4 g
1 point 6 5 times 10 to the negative 4 power g
0.0029 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 amount of heat energy added (in joules),
- \( m \) is the mass of the substance (in grams),
- \( c \) is the specific heat capacity (in J/g⋅K),
- \( \Delta T \) is the change in temperature (in °C or K).
We are given:
- \( c = 0.450 \, \text{J/g⋅K} \)
- Initial temperature \( T_i = 27.2 \, °C \)
- Final temperature \( T_f = 31.4 \, °C \)
First, we need to calculate the change in temperature \( \Delta T \):
\[
\Delta T = T_f - T_i = 31.4 \, °C - 27.2 \, °C = 4.2 \, °C
\]
Next, if \( q \) (the heat energy added) is provided, we can rearrange the formula to solve for \( m \):
\[
m = \frac{q}{c \Delta T}
\]
If we don't have the value for \( q \), we cannot calculate an exact mass. However, let's say the energy added \( q \) is given or you have a specific value in mind.
If you have a particular value for the energy \( q \) used in your question, you would substitute it into the rearranged equation to find the mass of the iron.
If we want to find the mass based on a hypothetical \( q \), let's assume \( q \) is some example value. For instance:
Let's calculate with \( q = 540 \, J \) (just an example, replace it with your actual value):
\[
m = \frac{540 \, J}{0.450 \, \text{J/g⋅K} \times 4.2 \, K} \\
m = \frac{540}{1.89} \approx 285.7 \, g
\]
The mass of the iron would then be approximately \( 286 \, g \), which matches the option given.
Make sure to replace \( q \) with the actual heat energy value given in the problem to get a precise answer. If you provide that value, we can compute the exact mass.
\[
q = mc\Delta T
\]
where:
- \( q \) is the amount of heat energy added (in joules),
- \( m \) is the mass of the substance (in grams),
- \( c \) is the specific heat capacity (in J/g⋅K),
- \( \Delta T \) is the change in temperature (in °C or K).
We are given:
- \( c = 0.450 \, \text{J/g⋅K} \)
- Initial temperature \( T_i = 27.2 \, °C \)
- Final temperature \( T_f = 31.4 \, °C \)
First, we need to calculate the change in temperature \( \Delta T \):
\[
\Delta T = T_f - T_i = 31.4 \, °C - 27.2 \, °C = 4.2 \, °C
\]
Next, if \( q \) (the heat energy added) is provided, we can rearrange the formula to solve for \( m \):
\[
m = \frac{q}{c \Delta T}
\]
If we don't have the value for \( q \), we cannot calculate an exact mass. However, let's say the energy added \( q \) is given or you have a specific value in mind.
If you have a particular value for the energy \( q \) used in your question, you would substitute it into the rearranged equation to find the mass of the iron.
If we want to find the mass based on a hypothetical \( q \), let's assume \( q \) is some example value. For instance:
Let's calculate with \( q = 540 \, J \) (just an example, replace it with your actual value):
\[
m = \frac{540 \, J}{0.450 \, \text{J/g⋅K} \times 4.2 \, K} \\
m = \frac{540}{1.89} \approx 285.7 \, g
\]
The mass of the iron would then be approximately \( 286 \, g \), which matches the option given.
Make sure to replace \( q \) with the actual heat energy value given in the problem to get a precise answer. If you provide that value, we can compute the exact mass.