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)
  $Q = W$
  or
  $\Delta Q = \Delta W$
  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
  

• Notes
  • Introduction to Thermodynamics
  • Concept of Heat
  • P-V Diagram
  • Work done by Gas in volume changes
  • Internal Energy
  • First Law of Thermodynamics
  • Specific Heat Capacity of Ideal GAS
  • Thermodynamic Processes
  • Quasi static Processes
  • Isothermal Process
  • Adiabatic Process
  • Isochoric process
  • Isobaric process
  • Cyclic process
  • Work done in Isothermal process
  • Work done in an Adiabatic process
  • Heat Engine and efficiency
  • Principle of a Refrigerator
  • Second law of thermodynamics
  • Reversibility and irreversibility
  • Carnot's Heat Engine
  • Carnot Theorem
  • Solved Examples
• Assignments
  • Thermodynamics Questions
  • Multiple Choice Questions
  • P-V diagram Problems and Solutions
  • Carnot Cycle Problems
• Revision Notes
  • Thermodynamics revision sheet