Conditions & Equations

Question 1

Isothermal Conditions=?

Answer 1

No change in temperature

Heat (q) can still change!

∆U=0 only if it is an ideal gas

Question 2

Isolated System

Answer 2

No exchange of matter with the surroundings

No exchange of energy with the surroundings

Question 3

Closed System

Answer 3

No exchange of matter with the surroundings

Exchanges energy with the surroundings

Question 4

Open System

Answer 4

Exchanges matter with the surroundings

Exchanges energy with the surroudnings

Question 5

Equation for Non-Expansion Work?

Answer 5

w=mgh

Question 6

Work:

General Equation?

Conditions for Equation?

Answer 6

W= -∫P_exdV

system must be reversible

Question 7

Heat:

General Equation?

Conditions for Equation?

Answer 7

q= ∫CdT

Process must be reversible

Note: C=constant, so q=CΔT

Question 8

Internal Energy:

General Equation?

Answer 8

ΔU= q + W

Question 9

Equation for Work at constant pressure?

Answer 9

W= -PΔV

Question 10

Equation for ΔU when volume is constant?

Answer 10

ΔU= q_v = C_vΔT

Question 11

Enthalpy:

General Equation

Equation @ constant pressure

Equation @ constant volume

Answer 11

ΔH= ΔU + Δ(PV)

ΔH= q_p

ΔH= ΔU + VΔP

Question 12

aH₂O_(l) —> aH₂O_(l) at constant pressure

Equation For:

q

w

ΔU

ΔH

Answer 12

q_p= nC_p,m(T_f-T_i)

w=0 (because change in V is negligible)

ΔU= nC_p,m(T_f-T_i)

ΔH= ΔU

Note: ΔH=ΔU=q_p

Question 13

aH₂O_(l) —> aH₂O_(l) at constant volume

Equation For:

q

w

ΔU

ΔH

Answer 13

q_v= C_v,mn(T_f-T_i)

w=0

ΔH = ΔU = q_v

Question 14

aH₂O_(l) —> aH₂O_(l) at constant Temperature

Equation For:

q

w

ΔU

ΔH

Answer 14

q=0

w=0 (because change in V is negligible)

ΔU=0

ΔH=0

Question 15

Adiabatic Conditions

Answer 15

No exchange of heat with the surroundings

Temperature can still change!

q=0

Question 16

aH₂O_(g) —> aH₂O_(g) at constant pressure

Equation For:

q

w

ΔU

ΔH

Answer 16

q_p= nC_p,m(T_f-T_i)

w= -nR(T_f-T_i)

ΔU= nC_v,m(T_f-T_i)

ΔH= nC_p,m(T_f-T_i)

Note: C_p,m=C_v,m+R

Question 17

aH₂O_(g) —> aH₂O_(g) at constant volume

Equation For:

q

w

ΔU

ΔH

Answer 17

q_v= nC_v,m(T_f-T_i)

w=0

ΔU=q_v

ΔH= n(C_v,m+R)(T_f-T_i)

Question 18

aH₂O_(g) —> aH₂O_(g) at constant temperature

Equation For:

q

w

ΔU

ΔH

Answer 18

q= -w= nRT ln(V_f / V_i)

w= -nRT ln(V_f / V_i)

ΔU=0

ΔH=0

Note: if given P instead of V, then w= -nRT ln(P_i / P_f)

Question 19

Phase Transitions:

aH₂O_(l) —> aH₂O_(g) at constant T & P

What is:

w

q

∆U

∆H

Answer 19

w= -P (V_(g) - V_(l))

q_p=∆H_transition (can be ∆H_vap , ∆H_fus , etc)

∆H_p=q_p

∆U= ∆H - PV_(g)

Question 20

Steps of the Carnot Cycle

Answer 20

1) Isothermal expansion
2) Adiabatic expansion
3) Isothermal compression
4) Adiabatic compression

Note: all state functions (for the whole process) are 0 because it’s a cycle

Question 21

Carnot Cycle

Total Work Equation?

Total Heat Equation?

Answer 21

W_total= -nRT_hot ln(V₂/V₁) - nRT_cold ln(V₄/V₃)

q_total = nRT_hot ln(V₂/V₁) + nRT_cold ln(V₄/V₃)

Question 22

General Equation for Entropy?

Answer 22

∆S=∫ dq_rev/T

Question 23

Equation for Efficiency?

Answer 23

E= w / q_hot

E= (q_h + q_c) / q_h

or

E= 1 + q_c /q_h

or

E= 1 - T_c / T_h

-for carnot cycle

Question 24

Gibbs free energy equation?

Answer 24

∆G= ∆H - T∆S

∆S_universe= -∆G_system / T