The temperature of an open room of volume 30 m³ increases from 17^oC to 27^oC due to the sunshine. The atmospheric pressure in the room remains 1 $$ \times $$ 10⁵ Pa. If N_i and N_f are the number of molecules in the room before and after heating, then N_f – N_i will be :

C_P and C_v are specific heats at constant pressure and constant volume respectively. It is observed that
C_P – C_v = a for hydrogen gas
C_P – C_v = b for nitrogen gas
The correct relation between a and b is

A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energy – time graph of the particle will look like:

A capacitance of 2 $$\mu $$F is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 $$\mu $$F capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is: