Applications of First Law: Concepts of Work, Heat & Energy | Physical Chemistry PDF Download

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
∵
 
⇒  
⇒ 
⇒ 
⇒ 
⇒     putting the value o f CV

⇒

⇒

Integrate this equation we get

Constant (C) = ln T + ln V^{r – 1} = ln TV^{r – 1} 
i.e. TV ^{r - 1} = constant 

 like this we can solve
PV^r = constant,  
i.e. for adiabat ic process
PV_^r = constant
V^{r – 1}T = constant
T^rP^{1 – r} = constant

where γ is atomicity and is equal to  

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 = - P_ext 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

where know in isothermal process

PV = constant
P₁V₁ = P₂V₂

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 = nC_PdT
when process is isothermal then dT = 0 then
dH = 0
dV = nC_VdT

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 = - P_ext dV

Let expansion of gas from volume V₁ and V₂ from pressure P₁ to P₂ then P₂ is external pressure:

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

P₁V₁ = nRT
P₂V₂ = nRT

and 

If expansion of gas from volume V₁ to V₂ & P₁ to P₂ against pressure P₃ then