An ideal gas, initially at 30°c and 100 kpa, undergoes the following cyclic processes in a closed system: (a) in mechanically reversible processes, it is first compressed adiabatically to 500 kpa, then cooled at a constant pressure of 500 kpa to 30°c, and finally expanded isothermally to its original state.

a) compressed adiabatically:

T2 = 576.8 K

ΔU = 3422 J/mol

b) cooled at P contant to 30°C:

Q = - 5965.04 J/mol

c) expanded isotermally to P=100 KPa:

W = - 4054.403 J

Explanation:

ideal gas in a mechanically reversible process:

∴ T1 = 30°C = 303 K

∴ P1 = 100 KPa

a) compressed adiabatically to 500 KPa:

⇒ ΔU = W = CvΔT(1)

∴ Cv = (3/2)R = 12.5 J/K.mol

∴ W = - PδV(2)

(1) = (2):

⇒ [(R+Cv)/R] Ln (T2/T1) = Ln (P2/P1)

∴ R+Cv/R = 5/2

⇒ (5/2) Ln(T2/T1) = 1.6094

⇒ LnT2 - LnT1 = 0.64376

⇒ LnT2 = 0.64376 + 5.7137 = 6.3575

⇒ T2 = 576.8 K

⇒ ΔU = W = (12.5 J/K.mol)(576.8 - 303 ) = 3422 J/mol

b)n cooled at constant P = 500KPa to 30°C:

∴ T2 = 303 K

∴ T1 = 576.8 K

∴ ΔU = Q + W

⇒ Q = CpΔT

∴ Cp = (5/2)R = 20.8 J/K.mol

⇒ Q = (20.8 J/K.mol)(303 - 576.8)

⇒ Q = - 5695.04 J/mol

c) expanded isothermally a P=100 KPa

∴ ΔU = 0

∴ T = 303 K

∴ P1 = 500 KPa

∴ P2 = 100 KPa

∴ W = nRT Ln(P2/P1)assuming n = 1 mol

⇒ W = (1 mol)(8.314 J/K,mol)(303 K) Ln(100/500)

⇒ W = - 4054.403 J

the molecules move in straight line until they collide with each other or with the walls of the container. collisions are perfectly elastic; when two molecules collide, they change their directions and kinetic energies, but the total kinetic energy is conserved.

explanation:

2fe + 3h2so4 -> fe2(so4)3 + 3h2

it is necessary to balance equations in order to get the proper amount of reactants as well as products in order not to make a miscalculation.

you cannot change the subscripts as that would change the substance itself. for instance, diatomic elements such as h2 only have the subscript two when a gas. another example would be so4, if you were to change the subscript, the element would no longer be sulfate.

we change the coefficients instead as that only changes the number of molecules rather than the substance itself.

hope this !