Quick Recap of Thermodynamics

Notes for Examination


Temperature

Relation between Celsius and fahrenhite scale is

T_F=9/5 T_C + 32°

T_F - Fahrenhite Temperature
T_C - Celsius Temperature

Relation between Celsius and kelvin scale is
T_C = T_K - 273.15 K


T_K - Temperature in Kelvin
T_C - Temperature in celsius


- If R₀ & R₁₀₀ are resistance of metak wire at ice and steam point resp then temp t can be defined corresponding to resistance R_T as follows

T =	(RT-R0)*100
	R100-R0

- The pressure,volume and temperature in kelvin of such gases obey the equation
PV=nRT ----(1)



Thermal expansion
ΔL=αLΔT


Specific Heat Capacity

c =	`Q
	nΔT

Gas Laws
Boyles Law: PV=constant
Charles Law : V/T=constant
Dalton Law of Partial Pressure: P=P₁ + P₂ +P₃
Root mean Square VelocityV_rms=√3RT/M
Mean Square Velocity
V_m=√8RT/&#960M
Average Velocity
V=√2RT/M
Also
V_rms > V_m > V

Average kinetic Energy of Gas=3/2nRT


First law of Thermodynamics

ΔU=Q-W


Gas Processes

Isothermal Process : PV=constant ,ΔU=0,Q=W,Molar Specific Heat=infinity
Adaibatic Process : PV^y=constant,Q=0,ΔU=-W,Molar Specific Heat=zero
Polytropic Process : PVⁿ=constant,Molar Specific Heat=R/y-1 + R/1-n
Volume Constant : P/T=constant W=0,ΔU=Q,Molar Specific Heat=C_v
Pressure Constant : V/T=constant ΔU=Q-W ,Molar Specific Heat=C_P

Internal energy depends on Temperature.
So for same temperature change ΔT
nC_vΔT=Q₁-W₁=Q₂-W₂=Q₃-W₃

Molar Specfic Heat Capacity of any process is given by

C=C_v + Pdv/ndT where n is no of moles of the gas

Workdone by Gas= ∫PdV



Heat Conduction

Q=-KAdT/dx

Wein displacement lawλT⁴=Constant

Stefan's Law
Q=eσT⁴

Newton law of Cooling

dT/dx=b(T-T_s)