Question

Two identical blocks of metal are at 20${}^o$C and 80${}^o$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 to the surroundings)?

• A. T${}_f$ will be 50${}^o$C
• B. T${}_f$ will be more than 50${}^o$C.
• C. T${}_f$ will be less than 50${}^o$C.
• D. T${}_f$ can be either more than or less than 50${}^o$C depending on the precise variation of the specific heat with temperature.

Answer 1

The correct option is D T${}_f$ can be either more than or less than 50${}^o$C depending on the precise variation of the specific heat with temperature.

$\text{Solution}:$

If specific heat is constant, then Total heat gain = 0

$ms(T_f–20)+ms(T_f–80)=0$

$\therefore T_f–20+T_f–80=0$

$\therefore T_f={50}^{o}C$

Now $T_f$ can be more than 50 or less than 50, depending on specific heat variation with temperature.

$\text{Hence D is the correct option}$