Specific Heat Capacity Units & Temperature Difference – Rankers Physics
Topic: Thermal Physics
Subtopic: Thermometer

Specific Heat Capacity Units & Temperature Difference

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

Solution:

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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