An ideal monatomic gas expands isothermally from state A to state B. The gas the

Question

An ideal monatomic gas expands isothermally from state A to state B. The gas then cools at constant volume to state C. The gas is then compressed isobarically to D before it is heated until it returns to state A. a) what is the internal energy of the gas at point B? b) what is the pressure of the gas when it is in state B? c) what is the temperature of the gas when it is in state C? The numbers are:

PA

PC

TA

= 10 atm

= 2 atm

= 327 degrees celcius

PA

PC

TA

= 10 atm

= 2 atm

= 327 degrees celcius

Explanation / Answer

State A:

V = 2 L

P = 10 atm

T = 600 K

State B:

V = 4L

T = 600 K

and since volume get twiced the pressure will be halved.

So P = 5 atm.

State C:

V = 4 L

P = 2 atm

Here Temperature will reduce in proportional to the pressure,

T = Tb/2.5 = 240 K

State D:

V = 2 L

P = 2 atm

So here the temperature will reduce in proportional to the volume.

T = Tc/2 = 120 K.

now coming to the question,

a) Number of moles of gas,

n = PV/RT,

at State A,

V = 2 L

P = 10 atm

T = 600 K

n = 2*10/(0.0821*600) = 0.406 moles.

So number of atoms, N = 0.406*6.022*10^23 = 2.44*10^23.

The internal energy at state B= (3/2)*N*k*T = 1.5*2.44*10^23*1.3807 x 10^(-23)*600 = 3032.02J = 3.03 kJ

b) Pressure of gas in state B, = 5 atm

c) Temperature in state C, = 240 K

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