write the expression for reversible work done.
Answers
Answer:
If the external pressure is zero, the work done is also zero as the gas expands into the vacuum. ... In the reversible process, Pext is always less than the pressure of the gas, by an infinitesimally small quantity. W = (P – dp) dV. In the equation W tends to the maximum as (P – dp) tends to P or dp tends to zero.
Answer:
ANSWER
Solution:-
Let us consider n moles of ideal gas enclosed in a cylinder fitted with a weightless and frictionless piston. The work of expansion for a small change of volume dV against the external pressure P is given by-dW=−PdV
∴ Total work done when the gas expands from initial volume V
1
to the final volume V
2
, will be-
W=−∫
V
1
V
2
PdV
For an ideal gas,
PV=nRT
⇒P=
V
nRT
Therefore,
W=−∫
V
1
V
2
V
nRT
dV
For isothermal expansion, T is constant.
Therefore,
W=−nRT∫
V
1
V
2
V
dV
⇒W=−nRT[lnV]
V
1
V
2
⇒W=−nRT(lnV
2
−lnV
1
)
⇒W=−nRTln(
V
1
V
2
)
⇒W=−2.303nRTlog(
V
1
V
2
).....(1)
At constant temperature,
P
1
V
1
=P
2
V
2
⇒
V
1
V
2
=
P
2
P
1
Therefore,
W=−2.303nRTlog(
P
2
P
1
).....(2)
Equation (1)&(2) are the expression for the work obtained in an isothermal reversible expansion of an ideal gas.
Explanation:
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