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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., P_{1}V_{1} = P_{2}V_{2}
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^{r}P^{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 V_{1} and V_{2} isothermal expansion.
W = – P dV
where know in isothermal process
PV = constant
P_{1}V_{1 }= P_{2}V_{2}
When V_{1} < V_{2} or P_{1} > P_{2} then expansion takes place and work is negative. When V_{1} > V_{2} or P_{1} < P_{2} then compression takes place & work is posit ive.
Energy in isothermal reversible process:
dH = nC_{P}dT
when process is isothermal then dT = 0 then
dH = 0
dV = nC_{V}dT
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 V_{1} and V_{2} from pressure P_{1 }to P_{2 }then P_{2} is external pressure:
W =  P_{ext }dV = –P_{2} (V_{2} – V_{1})
W = –P_{2} (V_{1} – V_{1})
P_{1}V_{1} = nRT
P_{2}V_{2} = nRT
and
If expansion of gas from volume V_{1} to V_{2} & P_{1} to P_{2 }against pressure P_{3} then
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