Question

Which has the capability to produce the most work in a closed system \(-1 \mathrm{kg}\) of steam at \(800 \mathrm{kPa}\) and \(180^{\circ} \mathrm{C}\) or \(1 \mathrm{kg}\) of \(\mathrm{R}-134 \mathrm{a}\) at \(800 \mathrm{kPa}\) and \(180^{\circ} \mathrm{C} ?\) Take \(T_{0}=25^{\circ} \mathrm{C}\) and \(P_{0}=\) 100 kPa.

Short answer

Answer: __________ (steam or R-134a)

Step-by-step solution

Determine the initial states of steam and R-134a

For both substances, we have the initial pressure P1 and temperature T1 given as 800 kPa and 180°C respectively. We can use these values to look up the necessary properties in the steam and R-134a tables.

Find the entropy and enthalpy values for the initial states of steam and R-134a

Using the steam tables and R-134a tables, find the entropy (s1) and enthalpy (h1) values for the initial states of both substances.

Determine the properties of the environment

As given in the problem, the environmental temperature T0 is 25°C, and the environmental pressure P0 is 100 kPa. We will use these values to determine the properties of the environment.

Calculate the specific exergy for steam and R-134a

The specific exergy (useful work potential) can be calculated using the following equation: \( e = (h_1 - h_0) - T_0(s_1 - s_0) - \frac{P_0(v_1 - v_0)} \) For both steam and R-134a, calculate the specific exergy using the previously found initial entropy, enthalpy, and environmental properties. Ensure units are consistent.

Compare the specific exergy values and determine which substance has the capability to produce the most work

Compare the calculated specific exergy values for steam and R-134a. The substance with the higher specific exergy value has the capability to produce the most work in a closed system.

Provide the final conclusion

Based on the comparison of specific exergy values, state which substance (1 kg of steam or 1 kg of R-134a) has the capability to produce the most work in a closed system under the given conditions.