Which of the following is/are not true about the heat capacity of a substance? (i) It is an intensive property…

To solve this question, we need to understand the definition and properties of Heat Capacity.

1. Analyze the Concepts

• Heat Capacity ($C$): This is the amount of heat required to raise the temperature of a body by one degree Celsius (or Kelvin). It is defined by the formula: $Q = C\Delta\theta$, where $Q$ is heat energy and $\Delta\theta$ is the change in temperature.
• Intensive vs. Extensive Properties: • Extensive properties depend on the amount of matter in the substance (e.g., mass, volume, heat capacity). If you have more of a substance, it takes more heat to raise its temperature. • Intensive properties do not depend on the amount of matter (e.g., density, specific heat capacity).
• S.I. Units: • Since $C = \frac{Q}{\Delta\theta}$, the unit is $\frac{\text{Joules}}{\text{Kelvin}}$, which is written as $JK^{-1}$. • $Jkg^{-1}$ is the unit for Specific Latent Heat, not Heat Capacity.

2. Evaluate the Statements

• (i) It is an intensive property: False. Heat capacity depends on the mass of the object, making it an extensive property.
• (ii) Its S.I unit is $JK^{-1}$: True. As derived from the formula $C = \frac{Q}{\Delta\theta}$.
• (iii) It is an extensive property: True. Because it depends on the quantity of the substance.
• (iv) Its S.I unit is $Jkg^{-1}$: False. This is not the unit for heat capacity.

3. Identify the "Not True" Statements

The question asks for the statements that are not true. Based on our evaluation:

• Statement (i) is not true.
• Statement (iv) is not true.

Therefore, (i) and (iv) are the statements that are not true.

4. Conclusion

Comparing our findings with the given options, the correct choice is C.

Exam Tip: Always distinguish between Heat Capacity (which depends on the whole object) and Specific Heat Capacity (which is a property of the material itself and is intensive). Remember: "Specific" usually means "per unit mass," which makes it intensive!