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## Homework Statement

Can someone help me confirm if I answered correctly please?

a) A sample of gas is enclosed in a cylinder by a piston. The cylinder is given 225J of energy which expands and pushes the piston 16cm outwards against an atmospheric pressure of 1.01x10

^{5}Pa.

i) give the equation for the first law of thermodynamics and clearly state the meaning of each symbol used.

ii) Show that for an enclosed fixed mass of gas, the change in work done, ΔW is equal to PΔV where P is the pressure of the gas and ΔV the change in volume.

iii) Assuming that the piston is friction less and has an area of 90cm

^{2}, calculate the external work done by the gas and the increase in internal energy of the gas.

b) An ideal gas of density 0.3kgm

^{-3}at 300K and pressure 1.5x10

^{5}Pa occupies a volume of 1.25x10

^{-3}m

^{3}. The gas first expands isobarically to a volume of 1.55x10

^{-3}m

^{3}and then it is compressed isothermally to its original volume.

i) What is isobaric expansion to its original volume.

ii) Calculate the energy added during the isobaric expansion.

iii) What is the temperature and pressure after the isothermal compression?

iv) Calculate the difference between the initial and final internal energy if the specific heat capacity of the gas at constant volume is 7x10

^{2}JkgK

^{-1}.

## Homework Equations

## The Attempt at a Solution

[/B]

ai) ΔU= ΔQ+ΔW

U is the internal energy of the system, Q is the heat gained or lost by the system and W is the work done by the system or on the system.

ii) W=PΔV

P = F/A = N/m²

V = m

^{3}

Si Units cancel out leaving "Nm"

W=F*s

iii) P=F/A

Force acting outwards:

F=PA

F=1.01x10

^{5}Pa*0.009m²

F=909N

W=Fs

W=909N*0.16m

W=145.44J

bi) Isobaric expansion, is an expansion in an enclosed gas system where the volume increases and the pressure is kept constant.

Isothermal compression involves the internal energy to be constant of an enclosed gas system, therefore we can derive that Q=-W. Heat applied to a system will be converted to work done. This process occurs under constant temperature therefore internal energy will remain constant.

ii) Since the first law of thermodynamics states that:

ΔU= ΔQ+ΔW

Work done: PΔV

W=1.5x10

^{5}Pa*3x10

^{-4}m

^{3}

W=45J

Loss in energy due to work done on the surroundings

I'm not sure how to find the change in heat energy, need advice on this one.

iii) Isothermal process takes place with a constant temperature.

So pressure:

p1v1=p2v2

1.5x10

^{5}Pa*1.55x10

^{-3}m

^{3}=p2*1.25x10

^{-3}m

^{3}

p2=186000Pa

During Isobaric expansion temperature wil increase to a point. After Isothermal process takes place the temperature will be the same.

Temperature:

V1/T1=V2/T2

1.25x10

^{-3}m

^{3}/300K=1.55x10

^{-3}m

^{3}/T2

T2=372K

v) Again i'm not sure about this one too.