Two identical blocks of same metal are $20^{\circ} C a n d 80^{\circ} C$ at respectively. Specific heat of the material of the two blocks increase with temperature. Which of the following is true about the final temperature $T_{f}$ when the two blocks are brought into contact?
(Assume that no heat is lost to the surroundings):

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$T_{f}$ will be less than $50^{\circ} C$

$T_{f}$ will be more than $50^{\circ} C$

$T_{f}$ will be either more than or less than $50^{\circ} C$ depending on the precise variation of the specific heat with temperature.

$T_{f}$ will be $50^{\circ} C$

answer is B.

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Detailed Solution

As temperature of second body is more, its average specific heat is more. In the formula $Δ Q = m s_{a v g} (Δ T), Δ Q$ and m are same for both. $Δ T$ is less for 2^ndone.
$(80 - T_{f}) < (T_{f} - 20)$
$100 < 2 T_{f} \Rightarrow T_{f} > 50^{\circ} C$