The thermodynamic process in which no work is done by the gas or on the gas is

The kinetic energy of an ideal gas is $E_0$ at $27^\circ\text{C}$. When the temperature is increased to $177^\circ\text{C}$, then kinetic energy will be

A particle executes a simple harmonic motion with a periodic time $8$ second. At time $t = 0$, it is at a mean position. The ratio of the distance traveled by a particle in the 2nd and that in the 1st second of its motion is
($\sin 45^\circ = \cos 45^\circ = \dfrac{1}{\sqrt{2}}$, $\sin 90^\circ = \cos 0^\circ = 1$)

The third overtone of a closed pipe of length '$L_c$' has the same frequency as the third overtone of the open pipe of length '$L_0$'. Both the pipes have same diameters. The ratio $L_c : L_0$ is equal to