NEET Physics Kinetic Theory of Gases MCQs

Two moles of an ideal monatomic gas undergo a process where $PV^3 = ext{constant}$. What is the molar heat capacity of the gas during this process?

An ideal monatomic gas undergoes a process following the equation $P = kV^{-3}$, where k is a constant. What is its molar heat capacity during this process?

For a monatomic ideal gas undergoing a process described by $PV^3 = ext{constant}$, the heat capacity at constant volume ($C_v$) is $\frac{3R}{2}$. What is the heat capacity ($C$) for this specific process?

An ideal monatomic gas undergoes a reversible polytropic process according to the relation $PV^x = ext{constant}$. If the molar heat capacity of the gas during this process is $R$, what is the value of $x$?

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature $T$ (Kelvin) and mass $m$, is

A neutron at thermal equilibrium with heavy water at $300$ K has a mass of $1.67 imes 10^{-27}$ kg. What is its de-Broglie wavelength? (Boltzmann constant $k_B = 1.38 imes 10^{-23}$ J/K, Planck's constant $h = 6.63 imes 10^{-34}$ Js)

If the de-Broglie wavelength of a neutron in thermal equilibrium is $2 imes 10^{-10}$ m, what is the temperature of the system? (Mass of neutron $m = 1.67 imes 10^{-27}$ kg, Boltzmann constant $k_B = 1.38 imes 10^{-23}$ J/K, Planck's constant $h = 6.63 imes 10^{-34}$ Js)

How does the de-Broglie wavelength of a neutron in thermal equilibrium change if the temperature is doubled?

Which of the following correctly represents the relationship between the de-Broglie wavelength ($\lambda$) of a neutron in thermal equilibrium and its mass ($m$) at a constant temperature?

4.0 g of a gas occupies 22.4 liters at NTP. The specific heat capacity of the gas at constant volume is $5.0 \, J K^{-1} mol^{-1}$. If the speed of sound in this gas at NTP is $952 \, m s^{-1}$, then the heat capacity at constant pressure is: (Take gas constant $R = 8.3 \, J K^{-1} mol^{-1}$)