In the figure a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. The lower compartment of the container is filled with 2 moles of an ideal monatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monatomic gas are $${C_v} = {3 \over 2}R$$, $${C_p} = {5 \over 2}R$$, and those for an ideal diatomic gas are $${C_v} = {5 \over 2}R$$, $${C_p} = {7 \over 2}R$$.
Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. Then total work done by the gases till the time they achieve equilibrium will be
A spray gun is shown in the below figure where a piston pushes air out of a nozzle. A thin tube of uniform cross-section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm, respectively. The upper end of the container is open to the atmosphere.
If the piston is pushed at a speed of 5 mm s$$-$$1, the air comes out of the nozzle with a speed of
A spray gun is shown in the below figure where a piston pushes air out of a nozzle. A thin tube of uniform cross-section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm, respectively. The upper end of the container is open to the atmosphere.
If the density of air is $$\rho$$a and that of the liquid $$\rho$$l, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to
Four charges Q1, Q2, Q3 and Q4 of same magnitude are fixed along the x axis at x = $$-$$2a, $$-$$a, +a and +2a, respectively. A positive charge q is placed on the positive y axis at a distance b > 0. Four options of the signs of these charges are given in List I. The direction of the forces on the charge q is given in List II. Match List I with List II and select the correct answer using the code given below the lists.
| List I | List II | ||
|---|---|---|---|
| P. | Q$$_1$$, Q$$_2$$, Q$$_3$$, Q$$_4$$ all positive | 1. | +x |
| Q. | Q$$_1$$, Q$$_2$$ positive; Q$$_3$$, Q$$_4$$ negative | 2. | $$ - $$x |
| R. | Q$$_1$$, Q$$_4$$ positive; Q$$_2$$, Q$$_3$$ negative | 3. | +y |
| S. | Q$$_1$$, Q$$_3$$ positive; Q$$_2$$, Q$$_4$$ negative | 4. | $$ - $$y |