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,


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 ...

1 year ago

Answered by Marcin, an IB Physics tutor with MyTutor

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


£36 /hr

James G.

Degree: Mathematical Physics (Doctorate) - Nottingham University

Subjects offered:Physics, Maths+ 2 more

Further Mathematics

“Currently a 3rd year PhD student in Mathematical Physics. I'm very passionate about teaching as well as my subject area. Look forward to hearing from you.”

MyTutor guarantee

£20 /hr

Ana S.

Degree: Physics (Bachelors) - Oxford, Balliol College University

Subjects offered:Physics, Maths+ 3 more

-Oxbridge Preparation-

“A friendly and understanding tutor with three years experience in school clubs, summer camps and private tutoring.”

£20 /hr

Quentin D.

Degree: Structural Engineering with Architecture (Bachelors) - Edinburgh University

Subjects offered:Physics, Science+ 2 more


“Hello! My name is Quentin Dorleans and I am a french IB graduate currently in my first year of studying Engineering at the University of Edinburgh. I am not a big study fan, and being extremely sporty myself I totally understand those ...”

About the author

£20 /hr

Marcin M.

Degree: Mechanical Engineering (Masters) - Edinburgh University

Subjects offered:Physics, Maths+ 1 more


“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

Describe the key difference between a scalar and a vector quantity

How would I write the binary number 11001 in decimal form?

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.

Suppose an object of mass 5kg is thrown horizontally from the top of a 100m cliff with initial velocity 2m/s, what is the horizontal displacement of the object after it hits the ground? (Air resistance negligible)

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