When the temperature of an ideal gas is increased by $600 \ K$,the velocity of sound in the gas becomes $\sqrt{3}$ times the initial velocity in it. The initial temperature of the gas is .... $^oC$

Statement $(I)$: Gas thermometers are less sensitive than liquid thermometers.
Statement $(II)$: The ratio of the universal gas constant and Avogadro's number is called Boltzmann's constant.
Statement $(III)$: The density of a given mass of a gas at constant pressure is inversely proportional to its absolute temperature.
The correct option among the following is:

An insulated box containing a diatomic gas of molar mass $M$ is moving with a velocity $v$. The box is suddenly stopped. The resulting change in temperature is

Which graph represents the molar heat capacity at constant volume $(C_V)$ for a monoatomic gas?

The mass of a hydrogen atom is $3.32 \times 10^{-27} \, kg$. If $10^{23}$ atoms per second strike a wall of area $2 \, cm^2$ at an angle of $45^{\circ}$ with the normal to the wall and reflect elastically with a speed of $10^3 \, m/s$,the pressure exerted on the wall will be: $(N/m^2)$

Which of the following graphs represents the variation of $\beta = -(dV/dP)$ with pressure $P$ for an ideal gas kept at a constant temperature?