Physics 2311. Thermodynamics material

Equations for Final Exam.

Constants, such as $R=8.314 J/mol\cdot K$ and $k_B=1.38\times 10^{-23}$ J/K, will be provided as needed.

19-2

One possible temperature conversion equation:

$$T_F = \frac{9}{5}T_C + 32^{\circ}F$$

19-4

Linear thermal expansion:

$$\Delta L = \alpha L_i \Delta T$$

19-6

Volume thermal expansion:

$$\Delta V = 3\alpha V_i \Delta T$$

19-8

Equation of State for an ideal gas:

$$PV = nRT$$

Variation: $P_i V_i = P_f V_f$ (Constant Temp. Called Boyle's Law).

20.4

Heat added to a liquid or solid:

$$Q = mc\Delta T$$

20.-

Heat capacity

$$C = mc$$

20-6

Latent heat of fusion or vaporization:

$$Q = \pm m L_{f~or~v}$$

20-8

Work done on a gas.

$$W = -\int_{V_i}^{V_f} PdV$$

20.9

First Law of Thermodynamics.

$$\Delta E_{int} = Q + W$$

20.-

First Law applied to special gas processes.

• adiabatic
  
  $$W=\Delta E_{int}$$
  
  

• isobaric
  
  $$W=-P\Delta V$$
  
  

• isothermal
  
  $$W=nRT \ln \frac{V_i}{V_f}$$
  
  

• isovolumetric
  
  $$W=0$$
  
  

20.14

Power of thermal conduction: (SKIP)

$${\cal P} = kA \vert\frac{dT}{dx} \vert$$

20.16

Power of thermal conduction, multi-slab problems: (SKIP)

$${\cal P} = A\frac{(T_h-T_c)}{\Sigma_i(L_i/k_i)}$$

20.18

Power of radiative emission: (SKIP)

$${\cal P} = \sigma A e T^4$$

21.2

Pressure in terms of mean molecular kinetic energy:

$$P = \frac{2}{3} \left( \frac{N}{V} \right)(\frac{1}{2}m\overline{v^2})$$

21.4

Mean translational KE related to temperature:

$$\frac{1}{2}m\overline{v^2} = \frac{3}{2} k_B T$$

21.7

Root Mean square speed:

$$v_{rms}= \sqrt{ \overline{v^2} }$$

21.8

Molar specific heat of ideal gas

• Constant volume: $Q = nC_V \Delta T$
• Constant pressure: $Q = nC_P \Delta T$

21.10

Total internal energy of ideal monatomic gas:

$$E_{int} = \frac{3}{2}nRT$$

21.12

Change in internal energy of ideal gas, any process:

$$\Delta E_{int} = nC_V \Delta T$$

21.16

Relation between $C_P$ and $C_V$:

$$C_{P}-C_V = R$$

21.18

Adiabatic process for ideal gas:

$$PV^{\gamma}=~constant$$

22.8

Entropy for some reversible process:

$$dS = \frac{dQ_r}{T} ~~~~~OR~~~~~ \Delta S = \int\frac{dQ_r}{T}$$

22.13

Entropy for adiabatic free expansion (or isothermal expansion) :

$$\Delta S = nR\ln \frac{V_f}{V_i}$$