Question

A sample of a monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A in the figure below). It is warmed at constant volume to 3.00 atm (point B). Then it is allowed to expand isothermally to 1.00 atm (point C) and at last compressed isobarically to its original state.

(a) Find the number of moles in the sample.
moles

(b) Find the temperature at point B.
K

(c) Find the temperature at point C.
K

(d) Find the volume at point C.
L

(e) Find Q, W, and ΔE_int for each of the processes.

	Q (kJ)	W (kJ)	Eint (kJ)
A → B
B → C
C → A

(f) For the whole cycle A → B → C → A, find Q, W, and ΔE_int.

Q	=  kJ
W	=  kJ
Eint	=  kJ

Answer 1

Given :

Volume at point A = V_{​​​​​​a}= 5 L = 5* 10^-3 m^{​​​​​​3}​​​

Temperature at point A = T_{​​​​​​a} = 300 K

Pressure at A P_{​​​​​​a} = 1 atm = 1* 1.013 * 10⁵ Pa

Part ( a)

Now using ideal gas equation

P* V = n *R*T

n = number of moles

P_{​​​​​​a} * V_{​​​​​​a} = n* R * T

1.013* 10⁵ * 5* 10^-3 = n * 8.314 * 300

n = 0.20 mole

part ( b)

Process A- B is carried out at constant volume

Now use below equation

P_{​​​​​​b}/ P_{​​​​​​a} = T_​​​b / T_{​​ a}

T _b = ( 3/1 ) * 300

T _b = 900 K

Part ( C)

Now process B- C is carried out at constant temperature

So the temperature at C is equal to temperature at B

T _{C =} T_{​​​​​​ b} = 900 K

part ( d)

Since process B- C is isothermal process

Now use below equation

P _b * V _b  = P ^{​​​​​​}_c * V _c

3 * 5* 10^-3 = 1* V _c ( Pb = 3atm , V _b = V_a = 5* 10^-3 m ³ )

V _c = 15 *10^-3 m^{​​​​​​ 3}

V _c = 15 L