Rank the volume of air in the glass, from greatest to least, when it is held a. near the surface as shown. b. 1 m beneath the surface. c. 2 m beneath the surface.
Solution 1R Introduction If we go deep inside the liquid, the pressure of the liquid increases with the depth. We will use this information and the ideal gas equation to calculate investigate the change in the volume. Solution Step 1 The pressure of the gas increases with the depth of the liquid. So the pressure on the air of the gas will be highest at 2 m beneath the water, at 1 m beneath the water the pressure will be less than 2 m and higher than surface of the water and it will be least at the surface. Step 2 From the ideal gas equation we know that PV = nRT Here P is pressure, V is volume, n is the mole, R is the ideal gas constant and T is the temperature of the gas. Now in the given problem, the temperature and the mole of the gas does not change, hence the right hand side of the above equation remains constant. So, the above equation can be written as PV = constant 1 V P Which means, if pressure of the gas increases, the volume decreases.