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Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE

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WORK, HEAT AND ENERGY

When process is isothermal: Ideal gas equation is: PV = nRT

When process is isothermal then 

PV = constant 
i.e., P1V1 = P2V2

When possible is adiabatic:

According to first law dq = dU – ω
dq = dU + Pdv                                     (ω = –Pdv)
⇒ dq = CV dT + pdv                               (dU = CVdT)
When process is adiabatic then dq = 0

i.e. 0 = CVdT + PdV

 Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE
⇒  Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE
⇒ Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE
⇒ Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE
⇒ Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE
⇒ Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE    putting the value o f CV

Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE

Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE

Integrate this equation we get

Constant (C) = ln T + ln Vr – 1 = ln TVr – 1 
i.e. TV r - 1 = constant 

 like this we can solve
PVr = constant,  
i.e. for adiabat ic process
PVr = constant
Vr – 1T = constant
TrP1 – r = constant

where γ is atomicity and is equal to Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE 

Isothermal process: Is of two type (1) reversible and irreversible

 

ISOTHERMAL WORK, HEAT AND ENERGY


(A)  When process is reversible: We know that in reversible process infinit e small change takes place i.e. integration will be possible in reversible process.

Work in reversible process: We know that
W = - Pext dV

where P is pressure & dV is change in vo lume it is posit ive.
Let expansion of gas from volume V1 and V2 isothermal expansion.
W = – P dV

 Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GREApplications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE

Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE
Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE
Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE
 

where know in isothermal process

PV = constant
P1V= P2V2

 Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE

When V1 < V2 or P1 > P2 then expansion takes place and work is negative.  When V1 > V2 or P1 < P2 then compression takes place & work is posit ive.

Energy in isothermal reversible process:
dH = nCPdT
when process is isothermal then dT = 0 then
dH = 0
dV = nCVdT

when process is isothermal then dT = 0 then
from first law, dq = dU – ω and
dU = 0 dq = –ω

Isothermal irreversible work, heat & energy: When process is irreversible then process is very fast and integration will not possible.

Work in irreversible process: 

W = - Pext dV

Let expansion of gas from volume V1 and V2 from pressure Pto Pthen P2 is external pressure:

W = - Pext dV = –P2 (V2 – V1)
W = –P2 (V1 – V1)

 Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE

P1V1 = nRT
P2V2 = nRT
Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE
and Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE

If expansion of gas from volume V1 to V2 & P1 to Pagainst pressure P3 then 

 Applications of First Law: Concepts of Work, Heat & Energy Notes | Study Chemistry for GRE Paper II - GRE

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