Question

two iron bolts of equal mass - one at 100 °c, the other at 55 °c - are placed in an insulated container. assuming the heat capacity of the container is negligible, what is the final temperature inside the container? (c of fe = 0.450 j/(g·k))

Explanation:

Step1: Set up heat - transfer equation

Let the mass of each bolt be $m$. The heat lost by the hot bolt is equal to the heat gained by the cold bolt. The heat transfer formula is $Q = mc\Delta T$. For the hot bolt at $T_{1}=100^{\circ}C$, the initial temperature is $T_{1}$ and the final temperature is $T_f$. For the cold bolt at $T_{2}=55^{\circ}C$, the initial temperature is $T_{2}$ and the final temperature is also $T_f$. The heat lost by the hot bolt $Q_1=mc(T_1 - T_f)$ and the heat gained by the cold bolt $Q_2=mc(T_f - T_2)$. Since $Q_1 = Q_2$, we have $mc(T_1 - T_f)=mc(T_f - T_2)$. The mass $m$ and specific - heat capacity $c$ cancel out.

Step2: Solve for $T_f$

We get $T_1 - T_f=T_f - T_2$. Rearranging the equation gives $2T_f=T_1 + T_2$. Substituting $T_1 = 100^{\circ}C$ and $T_2 = 55^{\circ}C$ into the equation, we have $T_f=\frac{T_1 + T_2}{2}$.

Step3: Calculate the final temperature

$T_f=\frac{100 + 55}{2}=\frac{155}{2}=77.5^{\circ}C$

Answer:

$77.5^{\circ}C$