Problem 34P

If 18.75 mol of helium gas is at 10.0°C and a gauge pressure of 0.350 atm, (a) calculate the volume of the helium gas under these conditions. (b) Calculate the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.

Solution 34PIntroductionIn this question, we shall have to consider Bernoulli’s principle. It states that mechanicalenergy of a fluid motion remains constant. This mechanical energy comprises of the fluid'spressure energy, kinetic energy and gravitational potential energy. It can be states as shownbelow.P + dv + hdg = constant…..(1), where P is the pressure at a point, d is the density of the 2fluid, h is the height of the point from the fluid’s surface.We shall also have to consider the continuity equation Av = constant, where A is the area ofcross-section and v is the fluid speed.Step 1Let P A is the pressure at the point A and v Ais the water speed at this point. Similarly, letP be the pressure at B and v be the liquid speed at B. B BSince all pipes are circular and in equal elevation, hence we can omit the gravitationalpotential energy term from the Bernoulli’s equation.For points A and B, it can be written as 1 2 1 2P A + 2v A = P B + 2v B 1 2 1 2P B = P A + 2v A 2v B d 2 2P B = P A + 2v A v B )…..(2)\n