The pressure P of a gas varies with distance z according to the relation P = (- z k_B ) , where k_B is the Boltzmann constant and is the absolute temperature. The SI unit of the constant is:

Step-by-step solution

According to the principle of dimensional homogeneity, the argument of the exponential function must be dimensionless. Therefore, the unit of is given by: Unit of = Unit of k_B Unit of z Since k_B represents thermal energy, its SI unit is Joule ( J ) or N m . The unit of distance z is meter ( m ). Unit of = N m m = N The exponential term as a whole is dimensionless, so the unit of pressure P must be equal to the unit of . Unit of = Unit of Unit of P Since the SI unit of pressure P is N m ⁻² , we have: Unit of = N N