Thermodynamics

Question 1

Thermal linear expansion

Answer 1

ΔL = αL_iΔT

Question 2

Thermal volumetric expansion

Answer 2

ΔV = βV_iΔT

Question 3

Relationship between volumetric expansion and linear expansion

Answer 3

β = 3*ɑ

for all isotropic solids

Question 4

ideal gas law

Answer 4

PV = nRT

or

PV=Nk_BT

• n -> number of moles*
• N -> number of molecules*
• k_B -> Boltzmann’s constant*

Question 5

Energy and temperature change relationship

Answer 5

Q = mcΔT

Question 6

Latent heat

Answer 6

Q = ± mL
energy required for a phase change

Question 7

Work to expand or compress gas

Answer 7

W = -∫PdV

Question 8

First law of thermodynamics

Answer 8

ΔE_int = Q + W

internal energy is equal to heat transfered and work done on the system

Question 9

Adiabatic process

Answer 9

No heat leaves or is added to a system
ΔE_int = W

Question 10

isobaric system

Answer 10

process occurs under constant pressure

W = -P(V_f - V_i)

Question 11

Isovolumetric system

Answer 11

Process that takes place under constant volumn

ΔE_int = Q

W = 0

Question 12

work done during isothermal expansion

Answer 12

W = n*R*T*ln(V_i/V_f)

Question 13

heat per second (power) transfered by coduction

Answer 13

P = kA|dT/dx|
|dT/dx| = (T_h - T_c)/L

Question 14

Pressure and molecular kinetic energy

Answer 14

P = 2/3*(N/V)*(1/2 m* v_avg²)

Question 15

Temperature and mean velocity

Answer 15

1/2 m*v_avg² = 3/2 k_bT

v_rms = sqrt(3RT/M) = sqrt(3k_bT/m)

Question 16

heat and temperature at constant volumn

Answer 16

Q = nC_VΔT

Question 17

heat and temperature at constant pressure

Answer 17

Q = nC_PΔT

Question 18

molar specific heat at constant volumn for ideal gas

Answer 18

C_V = 3/2*R

Question 19

ratio of specific heats in ideal gas

Answer 19

C_P - C_V = R

γ = C_P/C_V = 5/3

Question 20

Constant during adiabatic process

Answer 20

PV^γ = const

using ideal gas law:

TV^γ-1 = const

Question 21

Boltzmann distribution law

Answer 21

number of molecules at a certain energy

n_V(E) = n₀e^-E/k_bT

Question 22

rms velocity

Answer 22

v_rms = sqrt(3kT/m)

Question 23

average velocity of gas molecules

Answer 23

v_avg = sqrt(8kT/πm)

Question 24

most probable speed of gas molecules

Answer 24

v_mp = sqrt(2kT/m)

Question 25

mean free path of gas molecule

Answer 25

l = 1/(√(2)πd²n_V)

Question 26

collision frequency of molecules

Answer 26

f = √(2)πd²v_avgn_V = v_avg/l

Question 27

effeciency of heat engine

Answer 27

e = W_eng/|Q_h| = 1 -|Q_c|/|Q_h|

Question 28

Change in entropy (general)

Answer 28

dS = dQ_r/T

Q_r -> amount of energy transfered by heat in a reversible process

Question 29

Total change in entropy for carnot engine

Answer 29

0

Question 30

change in entropy for ideal gas

Answer 30

ΔS = nC_V*ln(T_f/T_i) + nR*ln(V_f/V_i)

Question 31

entropy of macrostate

Answer 31

S = k_bln(W)

W -> nuber of microstates of the system corresponding to mactrostate