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Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at 100 °C, while the other one is at 0°C. If the two bodies are brought into contact, then, assuming no heat loss, the final common temperature is:
A
less than 50 °C but greater than 0 °C
B
0 °C
C
50 °C
D
more than 50 °C
Explanation
The hotter body has the larger heat capacity, pulling the result above 50 °C.
Detailed Solution
Let θ be the final common temperature, and $s_c$, $s_h$ the average heat capacities of the cold and hot bodies ($s_c < s_h$).
Calorimetry: $s_h(100^\circ C - \theta) = s_c\theta$
$\theta = \frac{s_h}{s_h + s_c}\times100^\circ C = \frac{100^\circ C}{1 + s_c/s_h}$
$\because s_c/s_h < 1$, $1 + s_c/s_h \frac{100^\circ C}{2}$, i.e. θ > 50 °C
Calorimetry: $s_h(100^\circ C - \theta) = s_c\theta$
$\theta = \frac{s_h}{s_h + s_c}\times100^\circ C = \frac{100^\circ C}{1 + s_c/s_h}$
$\because s_c/s_h < 1$, $1 + s_c/s_h \frac{100^\circ C}{2}$, i.e. θ > 50 °C