Question

The specific heat of a material is given in a strange unit to be \(c=3.60 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{F}\). The specific heat of this material in the SI units of \(\mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C}\) is \((a) 2.00 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C}\) (b) \(3.20 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C}\) \((c) 3.60 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C}\) \((d) 4.80 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C}\) \((e) 6.48 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C}\)

Short answer

Answer: The specific heat of the material in SI units is 2.00 kJ/kg·°C.

Step-by-step solution

Recall the formula to convert Fahrenheit to Celsius

To convert the temperature from Fahrenheit to Celsius, the following formula can be used: \(\mathrm{T_{C}}=\frac{5}{9}\mathrm{(\mathrm{T_{F}}-32)}\)

Calculate the conversion factor for specific heat

Let a temperature difference of 1 degree Fahrenheit and convert it to Celsius: \( Δ\mathrm{T_{C}} = \frac{5}{9}(1-0) = \frac{5}{9}\) Now, we have the conversion factor for specific heat.

Convert specific heat to the SI unit

Use the conversion factor from Step 2 to convert specific heat from Fahrenheit to Celsius: \(c = 3.60 \frac{\mathrm{kJ}}{\mathrm{kg} \cdot^{\circ} \mathrm{F}} \times \frac{5}{9}= 2.00 \frac{\mathrm{kJ}}{\mathrm{kg} \cdot^{\circ} \mathrm{C}}\)

Identify the correct option

Comparing our calculated result to the given options, we find that our answer matches with option (a). Therefore, the specific heat of the material in SI units is: \(2.00 \frac{\mathrm{kJ}}{\mathrm{kg} \cdot^{\circ} \mathrm{C}}\).