The first Law of thermodynamics
LEARNING OBJECTIVES
There are following concept you will able to learn after reading this post -:
1. definition of first laws of thermodynamic
2. how conservation of energy is related to first laws of thermodynamics
3. calculation of work done by the gas
As we already know that heat is a form of energy . A system can be given heat either by supplying heat to it or by placing on a hotter body or gas stove . for understanding the transfer of energy from one body to other body . let us consider a system filled with water which is fitted with an outside cover on it head placed on a gas stove as shown in the diagram below . The heat is supplied by the gas stove to the bottom of the system , the water start to boil and vapour (gas) form during this process push the cover of the system . As the cover moves out , work is done by the gas on it and the gas loose this much amount of energy . Thus the gas gain energy as the heat is supplied to it and it loses energy as the work is done by it .
suppose in this process an amount Q of heat is given to the gas and an amount of w of work is done by it . Total energy of the gas must be increase by Q - w . In this way we can say that internal energy ( stored energy ) must be equal to Q - w . If we denote the change in internal energy by △U then we get -
△U = △Q - △w
⇒Q = △U +w This statement is applicable to any system
where
• △U = change in internal energy of the system.
• W = work interaction of system with its surrounding
•Q = algebraic sum of heat transfer between system and surrounding
This is the statement of the first laws of the thermodynamics .
First law of thermodynamics state that the change in internal energy of the system equal the net heat transfer into the system minus the net work done by the system .
point to be remember
•work done by the system is taken as positive (+)
•work done on the system is taken as negative (-)
•heat given to the system is taken as positive (+)
•heat given by the system is taken as negative (-)
△U will be positive if the temperature increases
△U will be negative if the temperature decreases
△U will be zero if the temperature remain constant
💥The first law of Thermodyamics is also related to as a conservation of energy because in this law only there is a transformation of energy from one form to another without any loss of energy . The total amount of energy and matter in the universe remain constant . In this way we can say that energy neither created nor destroyed in any process i.e energy remain conserve ( constant) . so the first laws of thermodymic is directly related to conservation of energy .
Note -:
👉for ideal gas internal energy is a function of temperature only .
👉 for isolated system internal energy always remain constant .
💢calculation of work done by gas
Work done by the gas takes place only when there is a change in volume of gas in any system
consider a gas contained in a cylinder of cross- sectional area A filled with a movable piston . let the pressure of the gas be p . The force exerted by the gas on the piston is PA in the outward direction . suppose a gas expand little and the piston is pushed out by a small volume△V .
Here △V = change in volume , p = external pressure exerted by piston on the cylinder
The work done by the gas on the piston
△W = ( P ). (△V) ( △V = A △X ) ; . , ∵ P = F/A ⇒ F = P.A
here A = Area of cross section of the cylinder
△X = the small distance moved by
Total work done by the gas in the process
W = ∫ P. (△V) , here taking integration from V 1 → V2 V1 = initial volume , V2 = final volume
unit of work = Force / Area * volume = Force / L.L * L.L.L = Force * L = N. m = joule (J)
1N.1m = 1J
work done by gas in an Isothermal process on an Ideal gas .
suppose an ideal gas has initial pressure , volume and temperature as p1 , V1 an T . In a process temperature remain constant and its pressure and volume changed from p1 to p2 and v1 to v2 .
Then the work done by gas is an shown in the figure .
work done by gas in Isobaric process .
suppose the pressure of a system remain constant at a value of p and volume changes from V1 to v2 . Then the work done by the system
W = ∫ pdv , here taking the integration from v1 to v2
W = p ∫ dv = p (v2- v1 )
work done by gas in Isochoric process .
In isochoric process the volume remains constant and no work is done by the system .
W = p* (V2-v1 )
W = 0 here change in volume = 0
There are following curve of different process .
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