5.0 g of nitrogen gas at 20 degree C and an initial pressure of 3.0 atm undergo

Question

5.0 g of nitrogen gas at 20 degree C and an initial pressure of 3.0 atm undergo an isobaric expansion unveil the volume has tripled. What are the gas volume and temperature after the expansion? How much heat energy is transferred to the gas to canes this expansion? The gas pressure is then decreased at constant volume until the original temperature is reached What is the gas pressure after the decrease? What amount of heat energy is Hans erred from the gas as its pressure decreases? Show the total process on a PV diagram. Provide an appropriate scale on both axes

Explanation / Answer

mol = mass/MW = 5/28 = 0.17857 moles of N"

T1 = 20C = 293 K P1 = 3 atm

volume will be:

PV = nRT --> V = nRT/P = (0.17857)(0.082)(293)/(3) = 1.430 Liters

Isobaric, P2 = 3 atm

so:

a)

Vnew = 3*V1 = 3*1.430 = 4.29 Liters

so

V1/T1 = V2/T2

T2 = V2/V1*T1

T2 = (3V1)/V1 * T1 = 3*T1 = 3*293 = 879 K

b)

Heat energy:

Q = n*C*(Tf-Ti)

C = 1.042 kJ/kg = 1.052 J / g = 1.062 J/g * 28 g / mol = 29.736 J/mol + 8.314 = 38.05 J/mol

Q = 0.17857 *(29.736+8.314) * (879 -293)

Q = 3981.62J = 3.981 kJ

c)

V2 = Vfinal

c)

gas pressure after decrease:

P2V2/T2 = P3V3/T3

3*4.29/(879) = P3*(4.29)/(293)

P3 = 3*4.29/(879)*293/4.29 = 1 atm

d)

Q = ?

Q = n*Cv*(Tf-Ti)

Q = 0.17857 *29.736*(293-879)

Q = -3111.63 J = -3.11 kJ

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