Question

An adiabatic capillary tube is used in some refrigeration systems to drop the pressure of the refrigerant from the condenser level to the evaporator level. \(\mathrm{R}-134 \mathrm{a}\) enters the capillary tube as a saturated liquid at \(70^{\circ} \mathrm{C}\), and leaves at \(-20^{\circ} \mathrm{C} .\) Determine the rate of entropy generation in the capillary tube for a mass flow rate of \(0.2 \mathrm{kg} / \mathrm{s}\).

Short answer

Based on the provided information about the refrigeration system using R-134a refrigerant, the rate of entropy generation in the capillary tube is calculated to be 0.153 kJ/s·K.

Step-by-step solution

Find the specific entropies at the inlet and outlet states.

To find the specific entropies at the inlet and outlet states, we need to consult the property tables for R-134a. Locate the entry for the saturated liquid state at 70°C and the state at -20°C to find the corresponding specific entropies. From the property tables, we find: - At 70°C, the specific entropy of saturated liquid R-134a, \(s_1 = 0.918\: \text{kJ/kg} \cdot\text{K}\). - At -20°C, the specific entropy of R-134a, \(s_2= 1.683\: \text{kJ/kg} \cdot\text{K}\).

Calculate the entropy change for the process.

Now that we have the specific entropies at the inlet and outlet states, we can calculate the entropy change: Entropy change, \(\Delta s = s_2 - s_1\) \(\Delta s = 1.683\: \text{kJ/kg} \cdot\text{K} - 0.918\: \text{kJ/kg} \cdot\text{K} = 0.765\: \text{kJ/kg} \cdot\text{K}\)

Determine the rate of entropy generation.

Finally, we will multiply the entropy change by the mass flow rate to find the rate of entropy generation: Rate of entropy generation, \(\dot{S} = \dot{m} \cdot \Delta s\) \(\dot{S} = 0.2\: \text{kg/s} \times 0.765\: \text{kJ/kg} \cdot\text{K} = 0.153\: \text{kJ/s} \cdot\text{K}\)

Present the final result.

The rate of entropy generation in the capillary tube for the given refrigeration system is \(\dot{S} = 0.153\: \text{kJ/s} \cdot\text{K}\).