Statements on Laws of Thermodynamics and Variable Types

To determine the correct combination of statements, let us analyze each statement individually:

1. Statement A: Zeroth law of thermodynamics gives concept of temperature

   • Analysis: The Zeroth Law of Thermodynamics states that if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This introduces the fundamental concept of a scalar property called temperature, which determines whether systems are in thermal equilibrium.
   • Status: True

2. Statement B: First law of thermodynamics gives concept of internal energy

   • Analysis: The First Law of Thermodynamics is a statement of the principle of conservation of energy: $\Delta Q = \Delta U + \Delta W$ It establishes the existence of a state function called internal energy ($\Delta U$).
   • Status: True

3. Statement C: In isothermal expansion of ideal gas, $\Delta Q \neq \Delta W$

   • Analysis: For an ideal gas undergoing an isothermal process, the temperature $T$ remains constant ($\Delta T = 0$). Since the internal energy of an ideal gas depends solely on its temperature, the change in internal energy is zero ($\Delta U = 0$). Applying the First Law of Thermodynamics: $\Delta Q = \Delta U + \Delta W \implies \Delta Q = \Delta W$ Therefore, the statement $\Delta Q \neq \Delta W$ is false.
   • Status: False

4. Statement D: Product of intensive and extensive variables is extensive

   • Analysis: Let an intensive variable be $I$ (which remains invariant when system size is scaled by a factor $\lambda$, i.e., $I \to I$) and an extensive variable be $E$ (which scales linearly with system size, i.e., $E \to \lambda E$).
   • The product $P = I \times E$ scales as: $P' = I \times (\lambda E) = \lambda (I \times E) = \lambda P$ Since the product scales proportionally with the system size, it is an extensive variable. For example, Pressure $P$ (intensive) $\times$ Volume $V$ (extensive) $= PV$ (work/energy, which is extensive).
   • Status: True

5. Statement E: The ratio of any extensive variable to mass will be an extensive variable

   • Analysis: When an extensive variable $E$ is divided by mass $m$ (which is also extensive), both quantities scale linearly with system size $\lambda$: $\frac{E'}{m'} = \frac{\lambda E}{\lambda m} = \frac{E}{m}$ Since the ratio remains invariant under scaling, it represents a specific property (e.g., specific volume $v = V/m$), which is an intensive variable, not extensive.
   • Status: False

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Conclusion

The correct statements are A, B and D Only.

Correct Option: C