An ideal gas at pressure $p$ is enclosed in a container that is placed in a reservoir at temperature $T$. If the volume of the gas is increased to two times its original value, then the new pressure $p^{\prime}=$ $\_\_\_\_$ $p$

Two metal rods $A$ and $B$ each of length 50 cm can diameter 4.0 mm are joined together at temperature $30^{\circ} \mathrm{C}$. What is the change in length of the combined rod at $230^{\circ} \mathrm{C}$ ? (Given, linear expansion coefficients of rods $A$ and $B$ are respectively, $2.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ )

Find the difference in temperature between the water at the top and the bottom of 20 m high waterfall assuming 10\% of the energy of fall is spent in heating the water (use, specific heat capacity of water $=4000 \mathrm{~J} \mathrm{kg}^{-1} \mathrm{~K}^{-1}$ and $g=10 \mathrm{~m} / \mathrm{s}^2$ )

Assertion (A) The zeroth law of thermodynamics leads to the concept of temperature.

Reason (R) The zeroth law states that two systems in thermal equilibrium with a third system are in thermal equilibrium with each other.

The correct option among the following is