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380 ENGINEERING THERMODYNAMICS

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Joule concluded this result from a series of experiments conducted with an apparatus simi-
lar to the one shown in Fig. 8.5.
— Two tanks connected by a valve were submerged in a bath of water.
— Initially one tank was evacuated and the other was filled with air under high pressure.
— A thermometer was placed in the water bath.
— After the tank and water had attained the same temperature, the valve between the
two tanks was opened to pass air slowly from high pressure tank to the evacuated tank.
Time was allowed for equilibrium to be attained.
Joule observed that there was no change in temperature of water during or after the process.
Since there was no change in the temperature of water, he concluded that there was no heat
transfer between air and water i.e., δQ = 0. And since there was no work during the process, i.e.,
δW = 0, from the first law of thermodynamics, δQ = dE + δW, Joule concluded that change in
internal energy of the air is zero, i.e., dE = 0.

Valve

Evacuated

tank

Air under

high

pressure

Thermometer

Bath of

water

Fig. 8.5. Apparatus for demonstration of Joule’s law.
Again, since both pressure and volume changed during the process, he remarked that inter-
nal energy was a function only of temperature ; since during the process temperature did not
change, the internal energy remained constant.
Later on when experiments were conducted with more refined instruments, it was found
that there was a very small change in temperature of water, indicating that for real gases internal
energy was not a function of temperature alone. However, at low pressure and high temperature
where real gases behave like semi-perfect gases and where the equation of state for a semi-perfect
gas, pv = RT, is sufficiently accurate, Joule’s law holds equally good in that range.
From definition of enthalpy,
h = u + pv
Also pv = RT
∴ h = u + RT ...(8.11)
Since u is a function of temperature only, h is a function of temperature,
i.e., h = f(T) ...(8.12)

8.5. Specific Heat Capacities of an Ideal Gas

The specific heat capacity at constant volume of any substance is defined by

cv =

∂

∂

u

T v

F

HG

I

KJ