- Home
- Standard 11
- Physics
Two identical blocks of metal are at $20^{\circ} C$ and $80^{\circ} C$, respectively. The specific heat of the material of the two blocks increases with temperature. Which of the following is true about the final temperature $T_f$ when the two blocks are brought into contact (assuming that no heat is lost to the surroundings)?
$T_f$ will be $50^{\circ} C$
$T_f$ will be more than $50^{\circ} C$
$T_f$ will be less than $50^{\circ} C$
$T_f$ can be either more than or less than $50^{\circ} C$ depending on the precise variation of the specific heat with temperature
Solution
(b)
When blocks are brought into contact, hotter one lost heat and colder one gains that heat.
Let $T=$ final temperature of the blocks.
Then,
Heat lost by hotter block $=$ Heat gained by colder block
$\Rightarrow m s_1\left(T_i-T_f\right)_{\text {Hot block }}=m s_2\left(T_f-T_i\right)_{\text {Cold block }}$
or $\frac{s_1}{s_2}=\frac{(T_f-T_i^T)_{\text {Cold block }}}{(T_i-T_f)_{\text {Hot block }}}$
Here, we are using two different specific heats $s_1$ and $s_2$ as it is given that specific heat of material increases with temperature. So, $s_1 > s_2$.
$\Rightarrow \frac{ s _1}{ s _2} > 1$
$\Rightarrow \frac{\left(T_f-T_i^{\top}\right)_{\text {Coldblock }}}{\left(T_i-T_f\right)_{\text {Hot block }}} > 1$
$\Rightarrow \frac{T-20}{80-T} > 1$
$\Rightarrow T-20 > 80-T$
$\Rightarrow T+T > 80+20$
$\Rightarrow 2 T > 100$
$\Rightarrow T > 50^{\circ} C$
