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?

343 g
0.0029 g
286 g
1.65*10^-4 g

Answers

GPT-4o mini
To find the mass of the iron piece, we can use the formula for heat transfer:

\[
Q = mc\Delta T
\]

where:
- \( Q \) is the heat energy added,
- \( m \) is the mass of the iron,
- \( c \) is the specific heat capacity,
- \( \Delta T \) is the change in temperature.

The specific heat \( c \) of iron is given as \( 0.450 \, \text{J/g}\cdot\text{K} \).

First, we calculate the change in temperature:

\[
\Delta T = T_{\text{final}} - T_{\text{initial}} = 31.4\, \text{C} - 27.2\, \text{C} = 4.2\, \text{C}
\]

Now substituting this into the formula, we have:

\[
Q = mc\Delta T
\]
\[
Q = m \cdot 0.450 \, \text{J/g}\cdot\text{K} \cdot 4.2 \, \text{K}
\]
\[
Q = m \cdot 1.89 \, \text{J/g}
\]

To find the mass of the iron, we need the value of \( Q \). However, since it's not provided, we cannot directly solve for mass.

To check the options provided:
- 343 g
- 0.0029 g
- 286 g
- \( 1.65 \times 10^{-4} \) g

Let’s calculate the expected mass for different \( Q \) values based on typical amounts of energy added, but since we don’t have \( Q \), we cannot definitively find mass in the absence of this value.

In practical scenarios, if a specified amount of energy was provided (for instance, 100 J or 10 J), we could calculate mass. Since the information about the energy \( Q \) is missing here, we cannot conclusively determine the correct answer among the provided options.

If you have a specific value for \( Q \), please provide it, and I can calculate the mass of the iron piece for you.