Question

1. What is the pressure at the bottom of Loch Ness, which is as much as 754 ft deep? Assume the density of the water is 1000 kg/m3 and the air above is at a pressure of 101.3 kPa.

2. A long steel beam has a length of twenty-eight meters on a cold day when the temperature is 0°C. What is the length of the beam on a hot day when T = 39°C? (α_steel = 1.1 × 10−⁵/C°)

3. A 2.00-L container holds half a mole of an ideal gas at a pressure of 12.0 atm. What is the gas temperature? show your work.

Answer 1

1) Gauge pressure due to liquid column is given by

Where is the density of liquid, h is height of liquid above that point and g is acceleration due to the gravity.

For absolute pressure( or total pressure) at the depth h, atmospheric pressure above the liquid surface will also be added

Here,

h=754 ft= 229.8 m (1m=3.281 ft)

Therefore total pressure is

P= 1000×9.81×229.8 + 101.3×10^3

P= 2.254×10^6 + 0.1013×10^6

P= 2.35×10^6 Pa