Q.A CLOSED COMPARTMENT CONTAINING GAS IS MOVING WITH SOME ACCELERATION IN HORIZONTAL DIRECTION.NEGLECT EFFECT OF GRAVITY. THEN PRESSURE IN THE COMPARTMENT IS

Pressure:

It is the force acting normally per unit area.

Pressure exerted by fluids:

Case I: (due to gravitational force acting in vertical direction)
       $P=\rho gh$
Here, $\rho$ is density of the fluid, g is acceleration due to gravity, and h is height of the fluid column.

Case II: (due to the external force acting in horizontal direction)
       $P=\rho ax$
Here, a is acceleration in horizontal direction and x is horizontal displacement.

Closed compartment is moving in horizontal direction with acceleration 'a':

This belongs to the case of external force acting in horizontal direction (case - II)

       Hence, $P=\rho ax$

Differentiate with respect to x.

             $\frac{dP}{dx}=-\rho a$

The negative sign implies that there is a fall in pressure as the compartment is accelerated 
in horizontal direction. In other words, when the compartment is accelerated in positive x
direction, then there is a decrease in pressure occurs in positive x direction.

Hence, the pressure in the compartment is smaller in front side.

Effect of opposite forces on the gas:

The opposite forces acting on the gas results some net force and it cause the gas to move.