Question

Specific heat is defined as the amount of energy needed to increase the temperature of a unit mass of a substance by one degree. The specific heat of water at room temperature is \(4.18 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C}\) in SI unit system. Using the unit conversion function capability of EES, express the specific heat of water in \((a) \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\) (b) \(\mathrm{Btu} / \mathrm{lbm} \cdot^{\circ} \mathrm{F}\) \((c)\) Btu/lbm-R, and (d) \mathrm{kcal} / \mathrm{kg} \(^{\circ} \mathrm{C}\) units.

Short answer

Question: Convert the specific heat of water from 4.18 kJ/kg*°C to (a) kJ/kg*K, (b) Btu/lbm*°F, (c) Btu/lbm-R, and (d) kcal/kg * °C. Answer: (a) In kJ/kg*K: c_water_a = \(4.18 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\) (b) In Btu/lbm*°F: c_water_b = Convert(c_water, 'kJ/kg*degC', 'Btu/lbm*degF') (c) In Btu/lbm-R: c_water_c = c_water_b (d) In kcal/kg * °C: c_water_d = Convert(c_water, 'kJ/kg*degC', 'kcal/kg*degC')

Step-by-step solution

Set up the specific heat in SI unit system

Given specific heat of water in SI unit system: c_water = \(4.18 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C}\)

Convert from SI to the desired units

Since we need to convert the specific heat into four different units, we will perform unit conversion for each desired unit using EES unit conversion function. (a) kJ/kg*K: The specific heat is already given in kJ/kg*°C, and since °Celsius and Kelvin scales have the same interval, the specific heat in kJ/kg*K will be equal to the given value: c_water_a = \(4.18 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\) (b) Btu/lbm*°F: EES has a built-in conversion function, Convert, which can be used to convert specific heat from one unit system to another. For converting the given specific heat to Btu/lbm*°F, we will use EES Convert function as follows: c_water_b = Convert(c_water, 'kJ/kg*degC', 'Btu/lbm*degF') (c) Btu/lbm-R: Since °Fahrenheit and Rankine scales have the same interval, the specific heat in Btu/lbm-R will be equal to the value obtained in step 2b: c_water_c = c_water_b (d) kcal/kg * °C: To convert the given specific heat to kcal/kg*°C, we will use EES Convert function as follows: c_water_d = Convert(c_water, 'kJ/kg*degC', 'kcal/kg*degC')

Record the results

We have successfully converted the specific heat of water into the desired units using the EES unit conversion function. (a) In kJ/kg*K: c_water_a = \(4.18 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\) (b) In Btu/lbm*°F: c_water_b = Convert(c_water, 'kJ/kg*degC', 'Btu/lbm*degF') (c) In Btu/lbm-R: c_water_c = c_water_b (d) In kcal/kg * °C: c_water_d = Convert(c_water, 'kJ/kg*degC', 'kcal/kg*degC')