Specific Heat Capacity Units & Temperature Difference – Rankers Physics

Thermometer: Practice Problem & Solution

Assertion (A): Specific heat capacity of a substance in \(\text{cal/g}^{\circ}\text{C}\) is greater than its specific heat capacity in \(\text{cal/g}^{\circ}\text{F}\). Reason (R): Magnitude (temperature difference) of \(1^{\circ}\text{C}\) is greater than the magnitude of \(1^{\circ}\text{F}\).  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Thermometer. Understanding the underlying formula is key to arriving at the correct answer below:

Reason (R) is true because a \(1^{\circ}\text{C}\) temperature change is equivalent to a \(1.8^{\circ}\text{F}\) change. Assertion (A) is true. Since \(c = \frac{Q}{m \Delta T}\) and \(1^{\circ}\text{C} = 1.8^{\circ}\text{F}\), \(c_{\text{cal/g}^{\circ}text{C}}\) will be \(1.8 \times c_{\text{cal/g}^{\circ}\text{F}}\) for the same substance. Therefore, (R) is the correct explanation of (A).

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