10.2 The Isothermal Expansion and Compression of an Ideal Gas

Energy of an ideal gas can only be changed by its…

temp

Isothermal process

temperatures of the system and the surroundings remain constant at all times

• ∆E = 0 

• q = -w 

free expansion

no heat flow or work is done

• P_external = 0

• the pressure against which the gas expands

irreversible process

even when a system is cycled (state 1 → state 2 → state 1) and thus returned to its original state, the surroundings are changed in a permanent way 

• P_ext < P_gas by a finite amount

Reversible Process

Both the system and surroundings are returned exactly to their original conditions

• system is always at equilibrium 

• P_ext≈ P_gas 

• w_rev = -nRT(V2/V1)

• q_rev = nRT(V2/V1)

Reversible Process Summary

Only when the expansion and compression are both done reversibly (by an infinite number of steps) is the universe the same after the cyclic process (the expansion and the subsequent compression of the gas go back to its original state)

• heat absorbed during the expansion = to heat released during compression

the maximum obtainable from a gas occurs when…

when the expansion is carried out reversibly 

• w_max = w_rev 

irreversible process summary

• more heat is released into the surroundings than is absorbed in the expansion process 

• Work (ordered energy) → heat (disordered energy)

• All real processes are irreversible 

  • Cant be carried out in a finite number of steps