Question

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is held at a temperature of ${100}^{0}C$ while the other one is kept at $0^{0}C$. If the two are brought into contact, then, assuming no heat loss to the environment, the final temperature that they will reach is

• A. ${50}^{0}C$
• B. Less than ${50}^{0}C$
• C. More than ${50}^{0}C$
• D. $0^{0}C$

Answer 1

The correct option is C More than ${50}^{0}C$

Let $\theta$ be the final common temperature.
Further, let $s_c$ and $s_h$ be the average heat capacities of the cold and hot (initially) bodies respectively (where $s_c<s_h$ given)
From, principle of calorimetry,
heat lost = heat gained
$s_h\left(100°C–\theta \right)=s_c\theta \Rightarrow \theta =\frac{s_h}{s_h+s_c}\times 100°C=\frac{100°C}{1+\frac{s_c}{s_h}}1+\frac{s_c}{s_h}<2\left(\because \frac{s_c}{s_h}<1\right)\therefore \theta >\frac{100°C}{2}or\theta >50°C$