Universiti Teknologi PETRONAS

Geoscience and Petroleum Engineering Department

PCB1043 Petroleum Engineering Thermodynamics

Dr Reza Ettehadi Osgouei ASSIGNMENTS-1

Date due: Oct 12.2011

Problem No: 1

A gas is contained in a piston-cylinder device at a given temperature and pressure. Heat is added and

the gas is allowed to expand at constant pressure to a new volume. If you were going to determine the

amount of work done and heat transferred, would you choose an open or closed system? Define your

system. Also show the process path on a P − V diagram.

Problem No: 2

A tank of compressed air is initially at 50 atm. A valve is opened and the pressure in the tank falls rapidly

to 30 atm. If you were to calculate the final temperature of the gas in the tank, how would you choose

the system?

Problem No: 3

A 10m3 tank contains nitrogen at 30 ◦C and 900 kPa. Some nitrogen is allowed to escape until the

pressure in the tank drops to 650 kPa. If the temperature at this point is 25 ◦C, determine the amount of

nitrogen that has escaped.

Problem No: 4

A pressure cooker cooks a lot faster than an ordinary pan by maintaining a higher pressure and

temperature inside. The lid of a pressure cooker is well sealed, and steam can escape only through an

opening in the middle of the lid. A separate piece of certain mass, the petcock, sits on top of this

opening and prevents steam from escaping until the pressure force overcomes the weight of the rocker.

The periodic escape of the steam in this manner prevents any potentially dangerous pressure buildup

and keeps the pressure inside at a constant value.

Determine the mass of the petcock of a pressure cooker whose operation pressure is 100 kPa gauges

and has an opening cross-sectional area of 5mm2. Assume an atmospheric pressure of 101 kPa.

Problem No: 5

A gas is contained in a vertical, frictionless piston-cylinder device as shown in the figure below. The

piston has a mass of 5kg and cross-sectional area of 25 cm2. A compressed spring above the piston

exerts a force of 75N on the piston. If atmospheric pressure is 98 kPa, determine the pressure inside the

cylinder.

Problem No: 6

Determine the mass and the weight of the air contained in a room whose dimensions are 10m×5m×

3m. clearly state your assumptions.

Problem No: 7

Sergei Bubka, world’s most famous pole vaulter, weighs 75 kg. Estimate the velocity of Bubka if he wants

to pass over a bar 6m high. Assume Bubka’s center of mass1 is initially 0.9m off the ground and reaches

its maximum height at the level of the bar itself. Indicate your assumptions.

Problem No: 8

Determine the work required for a 2000 kg car to climb a 100m long uphill road with a slope of 30ofor

the following cases:

a) At a constant velocity,

b) From rest to a final velocity of 30m/ s,

c) From 35m/ s to a final velocity of 5m/ s.

Problem No: 9

The potential energy function for the force between two atoms in a diatomic (two-atom) molecule can

be expressed in the form where x is the distance between the two atoms and a and b are positive

constants.

a) At what values of x is EP a minimum?

b) At what values of x is EP equal to zero?

c) Plot as a function of x.

d) Determine the force between the atoms.

e) The energy needed to break up the molecule into separate atoms is called the dissociation energy.

It is defined as the energy required to separate the two particles from their state of lowest energy to

x = ∞. Determine the dissociation energy.

Problem No:10

A potato initially at room temperature of 23 ◦C is being baked in an oven that is at 200 ◦C. Is there any heat transfer in this process? Problem No: 11 A 0.03m3 rigid container is open to the atmosphere and heat is added to the bottom of the container

until the air temperature inside reaches 450 ◦C. The container is then quickly sealed, removed from the

heating source and allowed to cool to room temperature of 20 ◦C. How much heat is lost during the cooling process?