First law of thermodynamics

First law of thermodynamics

  • Transfer of heat and performance of work are two mean of adding or subtracting energy from a system.
  • On transfer of energy, system is said to have undergone a change in internal energy.
  • Thus the sum of heat put into the system plus work done on the system equals increase in internal energy of the system for any process.
    if, $U_1$ is internal energy of state 1 and $U_2$ is internal energy of state 2 than change in internal energy would be
    $\Delta U=U_2 - U_1$
  • If W is the work done by the system on its surroundings then -W would be the work done on the system by the surroundings .
  • If Q is the heat put into the system then,
    Applying general law of conservation of energy $Q+(-W)= \Delta U$
    usually written as
    $Q=\Delta U + W$ --(1)
  • Equation (1) is then know as first law of thermodynamics and it can be applied when Q, W and U are expressed in same units.
  • Sometimes, we denote Heat and work by $\Delta Q$ and $\Delta W$,then $\Delta Q=\Delta U + \Delta W$ --(2)

Some Important things to remember about First law of Thermodynamics

  • $\Delta Q$ or Q is positive when heat is given to the system and Q is negative when heat is taken from the system
  • $\Delta W$ or W is positive when system expands and does work on surroundings
  • Hence we may say that when a certain amount of heat Q is given to the system then some part of it is used in increasing internal energy $\Delta U$ of the system while remaining part leaves the system in form of work done by the system on its surroundings.
  • From equation 4 we see that first law of thermodynamics is a statement of conservation of energy stated as
    ' The energy put into the system equals the sum of the work done by the system and the change in internal energy of the system'
  • If the system undergoes any process in which $\Delta U=0$ i.e., charge in internal energy is zero then from (1)
    $Q = W$
    $\Delta Q = \Delta W$
    that is heat supplied to the system is used up entirely in doing work on the surroundings.
  • If system reach from State A to state B by executing number of steps and $Q_1$, $Q_2$, $Q_3$ and $W_1$, $W_2$, $W_3$ are heat and work in each step, we can write the change of internal energy between state A and B as
    $ \Delta U= Q_1 + Q_2 + Q_3 - (W_1 + W_2 + W_3$
  • If the system returns to its original state after executing number of steps, the $ \Delta U=0$ and
    $Q_1 + Q_2 + Q_3 = W_1 + W_2 + W_3$
  • Equation (1) can be written as
    $ \Delta U= Q -W $
    Now since U being a thermodynamic state variable,it value does not depend on the path taken. but Q and W depends on the path . From the equation we can say that Combination of Q - W would be independent of the path

Solved Example

Question 1
A gas is given 50 Calorie of heat and Gas does the 20 J of work in the expansion resulting from heat given. Find the increase in the Kinetic energy of the gas in the process?
Q= 50 Calorie= 209 J
W= 20 J
From first law of Thermodynamics
$ \Delta U= Q -W $
$= 209 -20 = 189 J$

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