Home
Class 11
PHYSICS
Find the dimensions of a and b in the fo...

Find the dimensions of a and b in the formula `[P+ (a)/(V^(2))] [V-b]=RT` where P is pressure and V is the volume of the gas

Text Solution

Verified by Experts

By the principle of homogeneity, `a//V^(2)` is of the dimensions of pressure  and b is of the dimensions of volume.
[a] = [pressure] `[V^(2)]= [ML^(-1) T^(-2)] [L^(6)]= [ML^(5)T^(-2)]`
[b] `=[V]= L^(3)`
Promotional Banner

Topper's Solved these Questions

  • APPENDIX 1

    NCERT TAMIL|Exercise SOLVED EXAMPLE UNIT-2|9 Videos

  • APPENDIX 1

    NCERT TAMIL|Exercise SOLVED EXAMPLE UNIT-3|22 Videos

  • GRAVITATION

    NCERT TAMIL|Exercise ADDITIONAL EXERCISES|4 Videos

Similar Questions

Explore conceptually related problems

The volume of a cylinder is given by the formula V=pir^(2)h . Find the greatest and least values of V if r + h = 6.

In Vander Waal's gas equation (P + (2)/(V^(2))) (V-b) = RT. Determine the dimensions of a and b.

A monatomic ideal gas is contained in a rigid container of volume V with walls of total inner surface area A, thickness x and thermal conductivity K. The gas is at an initial temperature t_(0) and pressure P_(0) . Find the pressure of the gas as a function of time if the temperature of the surrounding air is T_(s) . All temperature are in absolute scale.

Two vessels A and B of equal volume (V_0) are connected by a narrow tube which can be closed by a value. The vessels are fitted with piston which can be moved to change the volumes. Initially, the valve is open and the vessels contain an ideal gas (C_p / C_v = gamma ) at atomspheric pressures (P_0) and atmoshpeheric temperature (T_0) . The walls of the vessels A are diathermic and those of B are adiabatic. The value is now closed and the pistons are slowly pulled out to increase the volumes of the of the vessels to dobuled the original value.(a) Find the temperatures and pressures in the two vessels. (b) The value is now opened for sufficeint time so that the gases acquire a common tempertures and pressures . Find the new values of the temperatuere and the pressures.

The dimensional formula of the constant ''a'' in Vanderwaals gas eqaution is (P+(a)/(V^(2)))(V-b)=RT :

Keeping the temperature as constant, a gas is compressed four times of its initial pressure. The volume of gas in the container changing from 20cc ( V_(1)" cc") to V_(2) cc. find the final volume V_(2) .