Problem 35P

What is the pressure inside a 35.0-L container holding 105.0 kg of argon gas at 385 K?

Solution 35PIntroductionThis question has to be solved using Torricelli’s theorem. This theorem establishes a relationbetween the speed of a liquid leaving a container through a passage and height of the passage.Torricelli’s theorem is a form of Bernoulli’s theorem.SolutionConsidering Bernoulli’s equation,P + dv 2+ dgh = P + dv 2 + dgh …..(1) 1 2 1 1 2 2 2 2Where, P and P are respective pressures at regions 1 and 2. These will be equal as they 1 2are atmospheric pressures. Now,v is t1e speed of the liquid through the hole. The liquidspeed in region 2 will be almost negligible (v 2 = 0). Since the passage is at the bottom,hence h w1ll be zero.h = 45 cm 2h = 0.45 m 2Density of water d = 1000 kg/m 3Therefore, from equation (1)P 1 + 1 × 1000 kg/m × v 12 + dg × 0 = P 2+ 1× 1000 kg/m × 0 + 1000 kg/m × 9.8 m/s × 0.45 m2 22 2500v 1 + 0 = 4410 2v 1 = 8.82v 1 3.0 m/sTherefore, the speed of water from the hole is approximately 3.0 m/s.