Thermodynamics of Black-Body Radiation - Revision history

Cosmo All at 23:18, 8 January 2013

2013-01-08T23:18:52Z

Igor: /* Problem 3 total number */

2012-11-19T20:15:04Z

‎Problem 3 total number

Igor at 11:39, 15 October 2012

2012-10-15T11:39:33Z

Igor at 11:36, 15 October 2012

2012-10-15T11:36:31Z

Igor: /* Problem 5 */

2012-10-15T11:31:29Z

‎Problem 5

Igor: /* Problem 4 */

2012-10-15T11:30:08Z

‎Problem 4

Igor: /* Problem 3 */

2012-10-15T11:29:45Z

‎Problem 3

Igor: /* Problem 2 */

2012-10-15T11:29:06Z

‎Problem 2

Cosmo All at 19:50, 1 October 2012

2012-10-01T19:50:18Z

Cosmo All at 20:33, 30 September 2012

2012-09-30T20:33:16Z

@@ Line 141: / Line 141: @@
      <p style="text-align: left;">The Planck distribution has maximum at frequency $\omega_m = 2.822 kT/\hbar.$ Then one obtains
 $ kT = 13.6/2.822 = 4.82\mbox{eV}$ and $T\approx 5.6 \cdot {10^4}\mbox{K}$.</p>
    </div>
 </div></div>

@@ Line 31: / Line 31: @@
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 3 total number ===
+=== Problem 3: total number ===
 Find the total number of photons.
 <div class="NavFrame collapsed">

@@ Line 1: / Line 1: @@
 [[Category:Cosmic Microwave Background (CMB)|1]]
+__TOC__
-−
-__NOTOC__
 <div id="bbrazm1"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 1: chemical potential ===
 Show that the photon gas in thermal equilibrium has zero chemical potential.
 <div class="NavFrame collapsed">
@@ Line 16: / Line 14: @@
-Now let us consider in the next 4 problems some volume $V$, filled with black-body radiation of temperature $T$.
+In the next 4 problems we consider some volume $V$, filled with black-body radiation of temperature $T$.
 <div id="bbrazm2"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 2 ===
+=== Problem 2: number density distribution ===
 Find the number of photons with frequencies in the interval $[\omega ,\omega +d\omega]$.
 <div class="NavFrame collapsed">
@@ Line 28: / Line 26: @@
    </div>
 </div></div>
@@ Line 34: / Line 31: @@
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 3 ===
+=== Problem 3 total number ===
 Find the total number of photons.
 <div class="NavFrame collapsed">
@@ Line 42: / Line 39: @@
    </div>
 </div></div>
@@ Line 48: / Line 44: @@
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 4 ===
+=== Problem 4: gas oven ===
 What is this number for a gas oven at room temperature and at maximum heat?
 <div class="NavFrame collapsed">
@@ Line 62: / Line 58: @@
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 5 ===
+=== Problem 5: energy distribution ===
 What is the energy of photons with frequencies in the interval $[ \omega ,\omega +d\omega]$?
 <div class="NavFrame collapsed">
@@ Line 75: / Line 71: @@
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 6 ===
+=== Problem 6: thermodynamic potentials ===
 Calculate the free energy, entropy and total energy of black-body radiation.
 <div class="NavFrame collapsed">
@@ Line 87: / Line 83: @@
 <div id="bbrazm6"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 7 ===
+=== Problem 7: thermal capacity ===
 Calculate the thermal capacity of black-body radiation.
 <div class="NavFrame collapsed">
@@ Line 99: / Line 95: @@
 <div id="bbrazm7"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 8 ===
+=== Problem 8: pressure ===
 Find the pressure of black-body radiation and construct its state equation.
 <div class="NavFrame collapsed">
@@ Line 111: / Line 107: @@
 <div id="bbrazm8"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 9 ===
+=== Problem 9: adiabatic equation ===
 Find the adiabatic equation for the black-body radiation.
 <div class="NavFrame collapsed">
@@ Line 123: / Line 119: @@
 <div id="cmb3"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 10 ===
+=== Problem 10: CMB as microwave ===
 Why CMB cannot be used to warm up food like in the microwave oven?
 <div class="NavFrame collapsed">
@@ Line 136: / Line 132: @@
 <div id="cmb6"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 11 ===
+=== Problem 11: Planck distribution ===
 The binding energy of electron in the hydrogen atom equals to $13.6\
 eV$. What is the temperature of the Planck distribution with this

@@ Line 16: / Line 16: @@
 <div id="bbrazm2"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 2 ===
-Find the number of photons with frequencies in the interval $[\omega ,\omega +d\omega]$ in a volume $V$ filled with black-body radiation of temperature $T$.
+Find the number of photons with frequencies in the interval $[\omega ,\omega +d\omega]$.
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
@@ Line 34: / Line 35: @@
 === Problem 3 ===
-Find total number of photons in the volume $V$ filled with black body radiation at temperature $T$.
+Find the total number of photons.
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
@@ Line 48: / Line 49: @@
 === Problem 4 ===
-Estimate the number of photons in a gas oven at room temperature and at maximum heat.
+What is this number for a gas oven at room temperature and at maximum heat?
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
@@ Line 62: / Line 63: @@
 === Problem 5 ===
-What is the energy of photons with frequencies in the interval $[ \omega ,\omega +d\omega]$, filling the volume $V$ at temperature $T$?
+What is the energy of photons with frequencies in the interval $[ \omega ,\omega +d\omega]$?
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
@@ Line 75: / Line 76: @@
 === Problem 6 ===
-Calculate free energy, entropy and total energy of black-body radiation.
+Calculate the free energy, entropy and total energy of black-body radiation.
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
@@ Line 82: / Line 83: @@
    </div>
 </div></div>
@@ Line 88: / Line 88: @@
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 7 ===
-Calculate thermal capacity of black-body radiation.
+Calculate the thermal capacity of black-body radiation.
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
@@ Line 95: / Line 95: @@
    </div>
 </div></div>
@@ Line 101: / Line 100: @@
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 8 ===
-Find pressure of black-body radiation and construct its state equation.
+Find the pressure of black-body radiation and construct its state equation.
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
@@ Line 108: / Line 107: @@
    </div>
 </div></div>
@@ Line 114: / Line 112: @@
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 9 ===
-Find adiabate equation for the photon gas of black-body radiation.
+Find the adiabatic equation for the black-body radiation.
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
@@ Line 121: / Line 119: @@
    </div>
 </div></div>
@@ Line 135: / Line 132: @@
    </div>
 </div></div>
@@ Line 142: / Line 138: @@
 === Problem 11 ===
 The binding energy of electron in the hydrogen atom equals to $13.6\
-eV$. What is the temperature of Planck distribution, with this
+eV$. What is the temperature of the Planck distribution with this
 average photon energy?
 <div class="NavFrame collapsed">

@@ Line 62: / Line 62: @@
 === Problem 5 ===
-Find energy of photons in black-body radiation of temperature $T$ in volume $V$, which have frequencies in the interval $\left[ \omega ,\omega +d\omega  \right]$.
+What is the energy of photons with frequencies in the interval $[ \omega ,\omega +d\omega]$, filling the volume $V$ at temperature $T$?
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
@@ Line 69: / Line 69: @@
    </div>
 </div></div>
 <div id="bbrazm5"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 6 ===
 Calculate free energy, entropy and total energy of black-body radiation.