Question

Two iron bolts of equal mass one at 100° C, the other at 55°C are placed in an insulated container, assuming heat transfer is negilble, what is the final temperature of the container? (c of iron =0.450 j/g* °C)

Answer 1

The temperature inside the container is 78 °C.

Explanation:

You don't give a heat capacity for the container, so I assume that it is perfectly insulated and absorbs no heat.

Then all that can happen is that the hot bolt radiates heat to the cold one until both are at the same temperature.

"Common" sense says that the final temperature should be half-way between the two extremes.

Let's see if this is so.

There are two heat transfers involved:

`"heat lost by bolt 1 + heat gained by bolt 2" = 0`

`color(white)(mmmmm)q_1 color(white)(mmm)+ color(white)(mmmmm)q_2 color(white)(mmmm)=0`

`color(white)(mmm)m_1C_1ΔT_1color(white)(m) + color(white)(mmm)m_2C_2ΔT_2color(white)(mml) = 0`

In this problem, `m_1 = m_2` and `C_1 = C_2`, so

`color(red)(cancel(color(black)(m_1C_1)))ΔT_1 + color(red)(cancel(color(black)(m_2C_2)))ΔT_2 = 0`

`ΔT_1 = ΔT_2`

`T_text(f)" - 100 °C + "T_text(f)" - 55 °C = 0"`

`2T_text(f) = "155 °C"`

`T_text(f) = "155 °C"/2 = "78 °C"`