MYTUTOR SUBJECT ANSWERS

688 views

1 dm^3 of water steam at 200 degrees C, 10 bar enters a compressor. When it leaves, its temperature is 400 deg. C and volume 0.5 dm^3. Calculate the final pressure of steam. Critically discuss the assumptions you made in your calculations.

This question refers to the behavior of gases under compression. In IB we model such situations using the ideal gas equation, which states that:

pV = nRT,

where:

p - pressure of the gas

V – its volume

n – number of moles of the gas

R – gas constant

T – temperature of the gas

We are given a description of the gas at two different states, so begin by writing down the equations for state 1 and state 2

p1V1 = n1R1T1

p2V2 = n2R2T2

Now notice that the amount of gas entering the compressor and leaving it should be the same, so n1 = n2 = n and of course the gas constant is the same in both cases (let’s just call it R).

So rewriting the equations again:

p1V1 = nRT1

p2V2 = nRT2

Rearranging them both to receive the expression for n”

n = (p1V1)/(RT1)

n = (p2V2)/(RT2)

Since this is the same n we can say that

(p1V1)/(RT1) =(p2V2)/(RT2)

The R is on both sides of the equation so we can cross it out:

(p1V1)/(T1) =(p2V2)/(T2)

We are asked to calculate p2, so rearrange this equation to obtain an expression for it:

p2 = (p1V1T2)/(T1V2)

So now we can just substitute the relevant values and get the final result, right? Well, not really, because if you have a closer look at them you will notice that they are not in SI units. We need to convert:

The temperatures to Kelvin:

T1 = 200 C = 473 K

T2 = 400 C = 673 K

Volumes to m^3:

V1 = 1 dm^3 = 0.001 m^3

V2 = 0.5 dm^3 = 0.0005 m^3

Pressures to Pa:

p1 = 10 Bar = 1000000 Pa

Now we can just plug then into the equation to get:

p2 = 2850000 Pa = 2.85 MPa

As you can see, both pressures are quite high (in the range of MPa). In our calculations we assumed that steam will behave like an ideal gas, i.e there will be no interactions between its molecules. At such pressures they will be so close together (remember your kinetic gas theory?), that they might indeed interact, so the results we got may not be a very good model of this situation. In fact, if you made measurements of pressure in states 1 and 2, you will find out that your results are off by approximately 10%.

Marcin M. IB Chemistry tutor, IB Maths tutor, IB Physics tutor, GCSE ...

2 years ago

Answered by Marcin, an IB Physics tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

16 SUBJECT SPECIALISTS

£24 /hr

Caroline D.

Degree: Theoretical Physics (Masters) - St. Andrews University

Subjects offered:Physics, Science+ 1 more

Physics
Science
Maths

“Theoretical Physics PhD at Max Planck Institute with first-class MPhys from St Andrews University. Passion and motivation for STEM, experienced in tutoring.”

£26 /hr

Ben J.

Degree: Physics and Computer Science (Natural Sciences) (Masters) - Durham University

Subjects offered:Physics, Science+ 6 more

Physics
Science
Maths
Further Mathematics
Computing
Chemistry
Biology
-Personal Statements-

“About Me: I'm a Physics and Computer Science student at Durham University, which sounds boring but it's actually really fun.I've got a great knack for making boring things more exciting, which is a good job given my degree title!  I'...”

Tomek E. GCSE Maths tutor, 11 Plus Maths tutor, IB Maths tutor, A Lev...
£20 /hr

Tomek E.

Degree: General Engineering (Masters) - Durham University

Subjects offered:Physics, Maths+ 2 more

Physics
Maths
Further Mathematics
-Personal Statements-

“Hi! I love helping people achieve their potential I can help you improve your Maths and Physics skills with sessions tailored to suit your needs!”

MyTutor guarantee

About the author

£20 /hr

Marcin M.

Degree: Mechanical Engineering (Masters) - Edinburgh University

Subjects offered:Physics, Maths+ 1 more

Physics
Maths
Chemistry

“About me I’m a Mechanical Engineering student at the University of Edinburgh, which means that I have to apply my knowledge of the subjects I tutor (Maths, Physics & Chemistry) on a daily basis. I graduated from an International Bacca...”

You may also like...

Posts by Marcin

1 dm^3 of water steam at 200 degrees C, 10 bar enters a compressor. When it leaves, its temperature is 400 deg. C and volume 0.5 dm^3. Calculate the final pressure of steam. Critically discuss the assumptions you made in your calculations.

In a lottery, 6 numbered balls are drawn from a pool of 59. Calculate the probability of scoring a jackpot. There used to be 49 balls in the pool. Calculate by how much the addition of 10 balls has decreased the probability of scoring a jackpot

Sort the following substances MgO, Na, H2O, H2S, NaCl, in the order of increasing melting temperature.

Other IB Physics questions

Define simple harmonic motion.

Why is centripetal acceleration directed inwards to the centre of the circle during centripetal motion? If I’m in a car while it’s cornering, I seem to be pushed outwards away from the centre, not inwards.

How do I do uncertainties properly?

When a hailstone of 0 C falls towards the earth, the kinetic energy of the hailstone is transferred to thermal energy in the ice. What is the minimum speed so that it just melts when it hits the surface. The latent heat of fusion of ice is 340 kJ/kg.

View IB Physics tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok