Question

Two copper bolts of equal mass - one at 82°C, the other at 21°C - are placed in an insulated container. Assuming the heat capacity of the container is negligible, what is the final temperature (in °C) inside the container (c of copper = 0.387 J/gK)? Enter to 0 decimal places.

Answer 1

Answer : The final temperature inside the container is, $51.5^oC$

Explanation :

In this problem we assumed that heat given by the hot body is equal to the heat taken by the cold body.

$q_1=-q_2$

$m_1\times c_1\times (T_f-T_1)=-m_2\times c_2\times (T_f-T_2)$

As per question, heat capacity of the container is negligible and mass is also equal. So, the formula will be:

$(T_f-T_1)=-(T_f-T_2)$

where,

$c_1$ = specific heat of copper

$c_2$ = specific heat of another copper

$m_1$ = mass of copper

$m_2$ = mass of another copper

$T_f$ = final temperature of mixture = ?

$T_1$ = initial temperature of copper = $82^oC$

$T_2$ = initial temperature of another copper = $21^oC$

Now put all the given values in the above formula, we get

$(T_f-82)^oC=-(T_f-21)^oC$

$T_f=51.5^oC$

Therefore, the final temperature inside the container is, $51.5^oC$