Question

A system is taken from state A to state B along two different paths 1 and 2. The heat absorbed and the work done by the system along these two paths are
(A) ${Q_1} - {W_1} = {Q_2} - {W_2}$
(B) ${Q_1} + {W_1} = {Q_2} + {W_2}$
(C) ${Q_1} = {Q_2}$
(D) ${W_1} = {W_2}$

Answer 1

Hint: This question can be solved using the first law of thermodynamics which is adapted for thermodynamic processes. This is based on the law of conservation of energy which states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but cannot be created nor destroyed.
Complete step by step solution:
 The heat absorbed and work done by the system alone the two paths are
${Q_1} + \left( { - {W_1}} \right) = {Q_2} + \left( { - {W_2}} \right)$
$ \Rightarrow {Q_1} - {W_1} = {Q_2} - {W_2}$

Hence option A is correct.

Additional information:
First law of thermodynamics: Energy of the universe remains constant, it cannot be created nor be destroyed even though energy can be exchanged between system and surroundings.
The second law of thermodynamics states that total entropy of an isolated system never decreases overtime and remains constant. This is applicable only if all the processes are reversible.
Third Law of thermodynamics states that entropy of a system at zero is well defined constant. It mainly decides the sign of entropy of a substance.
Entropy: It is usually defined as a measure of randomness or disorder of one particular system. It is an extensive property and it is a state function.

Note:
There are two statements related to the second law of thermodynamics. They are Kelvin-Planck Statement which states that if a heat engine is exchanging heat only with bodies at a single fixed temperature then it is impossible to produce a network in a complete cycle.
Clausius Statement: If a body is transferring heat from colder body to warmer body without consuming any work then it is impossible to construct a device operating in a cycle.
Entropy of fusion: It can be defined as a state where there is an increase in entropy when a solid melts into a liquid.
Entropy of Vaporization: It is the state where there is an increase in entropy when the liquid evaporates and changes into vapours.