Heat and Thermodynamics Notes

THERMOMETRY

Mercury is used as thermometric substance in liquid because it has low specific heat and high conductivity.

Absolute zero is 0K and -273.15⁰C.

Magnetic thermometer is used to measure very low temperature near absolute zero.

Thermocouple is used to measure rapidly changing temperature.

Pyrometer is used to measure temperature of Sun.

Gas thermometer are more sensitive than liquid thermometers as gas expands more than liquid.

To measure temperature most accurately we use constant volume gas thermometer.

Helium gas is used to measure very low temperature. 

Scale	LFP	UFP	FI
Centigrade	00C	1000C	1000C
Fahreinheit	320F	2120F	1800F
Kelvin	273K	373K	100K
Reumer	00R	800R	800R
Rankine	4920Ra	6720Ra	1800Ra

C-0/100 = F-32/180 = K-273/100 = R-0/80 = Ra-492/180

Relation between centigrade and Fahrenheit

C=5(F-32)/9

Faulty thermometer

Correct scale = Faulty scale

Or, X-LFP/UFP-LFP = Y-LFP/UFP-LFP

THERMAL EXPANSION

α: β: γ=1:2:3

L­ =L₀ (1 + α∆θ )

A = A₀ (1 + β∆θ)

V = V₀ (1 + γ∆θ )

  ρ= ρ₀ / (1 + γ∆θ)

 F=γ Aα∆θ

Expansion of liquid

  γ_r=γ_a + γ_g

fractional change in time period , ∆T/T = ½ α∆θ

temperature increases, length of pendulum increases, time period increases, clock  lose time.

If two rods are hollow and another solid heated

---->Through same temperature , equal expansion

----> same heat given , hollow rod expands more.

CALORIEMETRY

Specific heat capacity (S)= H/m∆θ  S for water = 4200 J/kg⁰ C

                                      S=0 for audible change

                                      S = infinity for isothermal change

Specific heat of hydrogen is largest among liquids and gases and water has largest among liquids.

When pressure increases, boiling point increases ( for all liquid)

                                                Melting point decreases ( for ice and rubber)

                                                Melting point increases ( for other solids)

Adding soluble impurities , boiling point increases

                                                Melting point decreases

Latent heat of fusion ----> ice = 80 cal / g

Latent heat of vapourization ---> water = 540 cal/g

Unit of water equivalent is kg/g.

KINETIC THEORY OF GAS

PV = nRT   n= m(mass)/M (molecular mass)

R =8.31 J/mol k  or , 2 cal/mol k

Boltzman constant (k) = R/N_A = 1.38 * 10^-23 J/k

pV = nkN_AT

pV = NkT (N=nN_A =Total number of molecules)

V_rms=√(3RT/M)

V_average = 0.921 x Rms velocity =√(8/π x RT/M )

V _{most probable speed} = 0.816 x Rms velocity = √(2 x RT/M)

Translational kinetic energy ,

T_K.E = ½ x mV² _rms = 3/2 kTN

HEAT TRANSFER

Q= (kAt(T₁-T₂ ))/L

where A= area of cross- sectional area, L = length of tube , T₁ and T₂  is temperature of two different point,

1 calorie = 4.2 joule

Conductor placement ,

In series,

• H_eq = H₁=H₂
• L_eq = L₁ +L₂
• A_eq = A₁ = A₂
• R_eq = R₁ + R₂

In series parallel,

• H_eq=H₁ + H₂
• L_eq =L₁=L₂
• A_eq = A₁ + A₂
• R_eq = R₁R₂/R₁+R₂

Convection is faster than conduction .

Radiation is fastest mode of heat transfer.

Q =R +A+T

a+r+t = O

when, t=0 , [a=1-r]  or  [r=1-a]

wien’s displacement law,

λT = 0.289 cm/s

βθϒϒE = sigma * temperature power 4

stefans law = 5.6 * 10 ^-8 W/m²K⁴

Newton’s law of cooling ,

(T₁-T₂) / t = k * ((T₁ + T₂ )/2 – T₀)

[ T₁ = initial temperature , T₂ = final temperature , t = time taken ,T₀ = surrounding temperature]

THERMODYNAMICS

Degree of freedom ,

• Monoatomic gas, f=3
• Diatomic gas , f=5
• Triatomic gas , f= 6

Internal energy (U)=f/2 nRT

Mayor’s formula , C_p – C_v  = R

C_p = (1+ f/2 ) *R

C_v = f/2 R

C_p / C_V = γ

γ = (1+ 2/f)

isochoric process , V= constant , ∆Q =∆U = f/2 x nRT = n C_V ∆T

isobaric process, p= constant , ∆ Q =∆U +∆W = f/2 nR∆T + r∆T

                                                            = nR∆T(f/2 +1)

                                                            = nC_v∆T

Isothermal process,  T= constant , ∆Q =∆W = nRT log_e(P1/p2)

                                    U = constant

Adiabatic process , Q = constant ,  ∆U =-∆W

Work done by the system or expansion is taken positive and work done on the system or compression is taken negative.

Adiabatic slope is steeper than isothermal slope.

• Isothermal process , PV= constant
• Adiabatic process , PV^γ = constant

First law of thermodynamics ,

∆Q = ∆ U + ∆ W

Second law of thermodynamics

,”heat can never flow from low temperature to high temperature without doing external work.” Clausius  statement.

Q₁ = Q₂ + W

Efficiency of heat engine,

F η = W/Q₁ x 100% = (Q₁-Q₂)/Q₁ x 100%

Q₁ =Q₂ +W

For refrigerator,

Coefficient of performance = Q₂/W = Q₂/(Q₁-Q₂)

[Q₁/Q₂ = T₁/T₂ ]

Boltzmann constant =R/N_A = 1.38 x 10^-23 Jk^-1

Average K.E. per molecule α Absolute temperature

Critical temperature is that temperature above which a gas can’t be liquefied by pressure only.

Gas possess greatest potential energy.

At boyle’s temperature real gas behaves as ideal gas.

Real gas show ideal behavior at low pressure and high temperature.

Volume of water is maximum at 4⁰ C.

(n₁ + n₂ )/γ_mean  = n₁ /(γ₁-1 )+  n₂/(γ₂ -1 )

Relative humidity increases increases = temperature decreases

Hygrometer measure R.H of air .

Triple point is point at which solid, liquid and gas of matter exist in equilibrium .

For water triple point is( 273.16K , 4.58 mm of Hg.