# First Law of Thermodynamics for a Control Mass (Closed System) Undergoing a Cycle

J.P. Joule conducted his experiments during 1840- 1849. His apparatus and experiments are shown in Fig. 4.1.

He took a fluid system (Fig. 4.1 (a)) and work wa.s done on the system by means of paddle wheel. The amount of work W = mgz. The temperature of the fluid system was increased. Now the system was placed in a water bath as shown in Fig. 4.1 (b). Heat Q was transferred to the water bath as seen through thermometer until the original state of the fluid was reached. The amount of heat transferred was measured from the increase in energy of water.

He then repeated the experiments by taking different systems and surroundings. Joul found that ratio of workdone on the system to heat generated was a constant. Mathematically.

Ф dW/ ф dQ=J=a constant called Joule’s constant

Or ϕdW = JϕdQ

If work and heat is expressed in the same unit (Joule) then

1J = 1Nm.

So ϕdW = ϕdQ

[symbol ϕ denotes the cyclic integral for closed path]

Now we can define first law of thermodynamics as “In a closed system undergoing cyclic operations, the network transfer is equal to net heat transfer”. Equation (4.1) is the mathematical formulation of first law for a closed system undergoing a cycle.