Following figure shows two processes A and B for a gas. If $$\Delta $$Q_A and $$\Delta $$Q_B are the amount of heat absorbed by the system in two cases, and $$\Delta $$U_A and $$\Delta $$U_B are changes in internal energies, respectively, then :

For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at 127°C. At 2 atm pressure and at 227°C, the rms speed of the molecules will be :

The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by :-

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to :
[Boltzmann Constant k_B = 1.38 × 10^–23 J/K Avogadro Number N_A = 6.02 × 10²⁶ /kg Radius of Earth : 6.4 × 10⁶ m Gravitational acceleration on Earth = 10ms^–2]