Question

A solid body $X$ of heat capacity $C$ is kept in an atmosphere whose temperature is $T_A=300K$. At time $t=0$ the temperature of $X$ is $T_0=400K$. It cools according to Newton's law of cooling. At time $t_1$ its temperature is found to be $350K$. At this time $t_1$ the body $X$ is connected to a larger body $Y$ at atmospheric temperature $T_A$ through conducting rod of length $L$ cross-sectional area $A$ and thermal conductivity $k$. The heat capacity of $Y$ is so large that any variation in its temperature may be neglected. The cross-sectional area $A$ of the connecting rod is small compared to the surface area of $X$. Find the temperature of $X$ at time $t=3t_1$.

• A. $T=300+50exp[-(\frac{kA}{LC}+\frac{\log 2}{t_1})2t_1]$.
• B. $T=400+50exp[-(\frac{kA}{LC}+\frac{\log 2}{t_1})2t_1]$.
• C. $T=350+50exp[-(\frac{kA}{LC}+\frac{\log 2}{t_1})2t_1]$.
• D. $T=300+60exp[-(\frac{kA}{LC}+\frac{\log 2}{t_1})2t_1]$.

Answer 1

The correct option is A $T=300+50exp[-(\frac{kA}{LC}+\frac{\log 2}{t_1})2t_1]$.