Two moles of nitrogen, N 2 , are under standard conditions. They are then transformed isothermically into a certain state and then quasi-statically and adiabatically into a finite state with a volume that is four times the initial one. Find the work performed by the gas if Q = 11300 J of heat was transmitted to the gas in the isothermal process.
Text Solution
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Sol. Let us determine the intermediate and final macro-states of the system. The ideal gas law results in an indeterminate system of equations. Let us employ the first law of thermodynamics in the form (29.11). For the isothermal process.
Q = W 1 = 
= 
RT 0 
= 
RT 0 ln 
,
where W 1 is the work done by the gas in the isothermal process. This enables us to find the volume that the gas must occupy in the intermediate state:
V 2 = V 0 e QM/mRT .
Next, using the equation governing an adiabatic process,
T 0 V 2 γ –1 = T 3 (4V 0 ) γ –1 ,
with γ = C p /C v the molar heat capacity ratio (commonly known as the specific heat ratio), we can find the final temperature:
T 3 = T 0 
.
Formula (29.6) yield the following expression for the internal-energy variation:
Δ U = 
(T 3 – T 0 ) = 
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