Embibe Experts Solutions for Chapter: Thermal Properties of Matter, Exercise 1: KEAM 2019

The standard of length is maintained by a $1 \mathrm{m}$ long bar made up of a material having coefficient of linear expansion $\alpha =0.00001°{\mathrm{C}}^{-1}.$ If the length of the bar were to be preserved to an accuracy of $1$ part per million, what would be maximum allowed temperature variation ?

Two identical systems, with heat capacity at constant volume that varies as $C_v=b{T}^3$ (where $b$ is a constant) are thermally isolated. Initially, one system is at a temperature $100 K$ and the other is at $200K$ . The systems are then brought to thermal contact and the combined system is allowed to reach thermal equilibrium. The final temperature (in $K$ ) of the combined system will be

Two taps supply water to a container, one at the temperature of $20°\mathrm{C}$ at the rate of $2\mathrm{kg}/\mathrm{minute}$ and another at $80°\mathrm{C}$ at the rate of $1\mathrm{kg}/\mathrm{minute}$. If the container gets water from the two taps simultaneously for 10 minutes, then the temperature of water in the container is