Question

The system is taken from state A to state B along 2 different paths 1 and 2. The heat absorbed and work done by the system along these 2 paths are \[{Q_1}{Q_2}\] and
\[{W_1}{W_2}\]
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: Apply the first law of thermodynamics to solve the sum which states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy.

Complete step by step solution:
To solve the sum, we need to consider the first law of thermodynamics.
The formula for the first law is as follows:
\[\Delta U = Q - W\]
Another formula for thermodynamic processes is:
\[{U_0} = {U_1} + {U_2}\]
Where, \[{U_0}\]denotes the internal energy of the combined system and \[{U_1} + {U_2}\]denote the internal energies of the respective separated systems.

Given, a system is taken from state A to state B along 2 different paths 1 and 2. The heat absorbed and work done by the system along these 2 paths are \[{Q_1},{Q_2}\]and \[{W_1},{W_2}\]

By the first law of thermodynamics,
\[{Q_1} + ( - {W_1}) = {Q_2} + ( - {W_2})\]
Hence, \[{Q_1} - {W_1} = {Q_2} - {W_2}\]is the answer.
Therefore, the correct option is option (a) i.e. \[{Q_1} - {W_1} = {Q_2} - {W_2}\]

Additional information:
The first law of thermodynamics is a form of the law of conservation of energy, which has been adapted for thermodynamic processes. It refers to distinguishing two kinds of transfer of energy, as heat and as thermodynamic work and relating them to a function of the body’s state is called internal energy.
According to the law of conservation of energy, the total energy of an isolated system is constant: energy can be transformed from one form to another and it can neither be created or destroyed.

Note: To solve the sum students first need to understand the meaning of the different laws of thermodynamics. Students also need to be able to write the formulas for the different laws of thermodynamics.