Common Formulas Used In Thermodynamics
1.)
- Relation between different scales of temperature.
TC = Celsius Temperature
TF = Fahrenheit Temperature
TR = Rankine scale Temperature
TK = Kelvin scale Temperature ( Div Sign below as under NR Pls note)
TC-0 = TF-32 = TR-0 = TK-273.15
100 180 80 100
2.) TC = 5/9 (TF-32)
3.) TF = 9/5 TC+32
4.) -40° C has same value on Celsius and Fahrenheit scale.
5.) Triple point of water on Absolute scale of Temperature is 273.16K
6.) There are 3 number of expansion coefficients
– coefficient of linear expansion
– coefficient of superficial expansion
– coefficient of cubic expansion
(a) coefficient of linear expansion
α = △l
l△T
new length, l’ after thermal expansion is
l’ = l (1+α △T)
(b) coefficient of superficial expansion
β = △SG
S△T
S’ = S(1 + β△T)
(c) coefficient of cubic expansion
γ = △V
V△T
Similarly New Volume
V’ = V(1 + γ△T)
(d) Relation between α, β, γ
6α = 3β = 2γ
or α = β = γ
2 3
7.) Heat supplied to a social mass m for increasing temperature △T is Q=m C △T(no face change)
8.) Heat supplied to change its state at constant temperature
Q = mL
9.) Gases posses infinite value of specific heat, But we consider only two specific heats Cp and Cv
Cp – specific heat at constant pressure
Cv – specific heat at constant volume
10.) Mayer’s formula
Cp – Cv = R R = Gas constant
11.) Degree of freedom of monoatomic and diatomic gas.
For monoatomic gas f= 3
(3 number of translational freedom)
For diatomic gas f= 5
(3 number of translational and 2 number of rotational freedom)
12.) For monoatomic gas f= 3
Cv = 3/2 R
Cp = 5/2 R
γ = 5/3 (Cp/Cv) = 1.67
13.) For diatomic gas f = 5, at room temperature
Cv = 5/2 R
Cp = 7/2 R
γ = 7/S (Cp/Cv)= 1.4
14.)For Triatomic gas f= 6
Cv = 3R
Cp = 4R
γ = 4/3 (Cp/Cv) = 1.33
15.) Rise in temperature of the body when it calls through height ‘h’
△T = g h
CJ
16.) Joules Mechanical Equivalent of Heat
J = W(Work)
Q(Heat) = 4.186 J/cal
W in Joules
Q in calories
17.) The height from when a block of ice be dropped that it melts on completely reaching the ground.
h = JL
g
18.) Equation of isothermal process
PV = constant
19.) Equation of adiabatic process
(i) PVγ = constant
(ii) TPγ-1 = constant
(iii) Tγ
Pγ-1 = constant
20.) Work done during Isothermal process
W = 2.303 RT log10 (V2/V1)
W = 2.303 RT log10 (P2/P1)
21.) Work done during adiabatic process
W =R/ γ-1 [ (T1-T2)]
W = R (P1V1-P2V2) —-DIV sign under R
γ – 1
W = Cv (T1-T2)
22.) Slope of a diabatic process graph is γ- times more than slope of Isothermal process.
23.) First Law of Thermodynamics
dq = du + dw
24.) Efficiency of Heat Engine
ɳ = 1 – Q2 (Div Sign Under Q2) Q1-heat extracted from
Q1 high temperature
source
ɳ = 1 – T2 (DIV SIGN UNDER T2) Q2-heat rejected
T1 To low
Temperature
sink.
T1-source
Temperature
T2-sink
Temperature
Efficiency of Heat engine can never be 100%
25.) coefficient of performance of a Refrigerator
β = T2 = Q2
( T1-T2) (Q1-Q2)
26.) There are two dead centers per cycle for a st.engine.
