Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 5.3-14

THE EXTREMUM PRINCIPLE IN THE LEGENDRE TRANSFORMED REPRESENTATIONS

Physics — Statistical Mechanics · maximum-work-thermodynamic-process

Problem

For a particular system (of 1 mole) the quantity

(v + a)f

is known to be a function of the temperature only (

= Y(T)

). Here

v

is the molar volume,

f

is the molar Helmholtz potential,

a

is a constant, and

Y(T)

denotes an unspecified function of temperature. It is also known that the molar heat capacity

c_v

c_v = b(v)T^{\frac{1}{2}}

where

b(v)

is an unspecified function of

v

a

) Evaluate

Y(T)

and

b(v)

b

) The system is to be taken from an initial state

(T_0, v_0)

to a final state

(T_f, v_f)

. A thermal reservoir of temperature

T_r

is available, as is a reversible work source. What is the maximum work that can be delivered to the reversible work source? (Note that the answer may involve constants unevaluated by the stated conditions, but that the answer should be fully explicit otherwise.)

Related theory

Work And Kinetic Energy Work Energy Theorem

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