Question

100 grams of \(R-134 a\) initially fill a weighted pistoncylinder device at \(60 \mathrm{kPa}\) and \(-20^{\circ} \mathrm{C}\). The device is then heated until the temperature is \(100^{\circ} \mathrm{C}\). Determine the change in the device's volume as a result of the heating.

Short answer

Answer: The change in volume of the piston-cylinder device is 0.01995 m³.

Step-by-step solution

Convert temperature to Kelvin

To be consistent with thermodynamic tables, convert the temperature from Celsius to Kelvin by adding 273.15 to each given temperature: Initial temperature: \(T_1 = -20^{\circ} \mathrm{C} + 273.15 = 253.15 \mathrm{K}\) Final temperature: \(T_2 = 100^{\circ} \mathrm{C} + 273.15 = 373.15 \mathrm{K}\)

Calculate the mass of R-134a

Given the amount of R-134a in grams, we need to convert it into mass (m) in kilograms: \(m = \frac{100 \mathrm{g}}{1000\, \mathrm{g/kg}} = 0.1 \mathrm{kg}\)

Determine the initial and final specific volumes from the R-134a tables

To find the initial and final specific volumes (\(v_1\) and \(v_2\)), we need to use the thermodynamic property tables for R-134a (found in most thermodynamics textbooks or engineering resources). Look up the specific volume values corresponding to the initial and final states, using the given pressure and temperature values: \(P_1 = 60 \mathrm{kPa}\) and \(T_1 = 253.15 \mathrm{K}\) \(P_2 = P_1 = 60 \mathrm{kPa}\) (Since the piston is weighted, the pressure remains constant during the heating process) and \(T_2 = 373.15 \mathrm{K}\) Find the corresponding specific volumes from the R-134a tables: \(v_1 = 0.1929\, \mathrm{m^3/kg}\) \(v_2 = 0.3924\, \mathrm{m^3/kg}\)

Calculate the initial and final volumes

Now that we have the specific volumes and mass of R-134a, we can calculate the initial and final volumes (V1 and V2) by multiplying the specific volumes by the mass of R-134a: \(V_1 = m \cdot v_1 = 0.1\, \mathrm{kg} \cdot 0.1929\, \mathrm{m^3/kg} = 0.01929\, \mathrm{m^3}\) \(V_2 = m \cdot v_2 = 0.1\, \mathrm{kg} \cdot 0.3924\, \mathrm{m^3/kg} = 0.03924\, \mathrm{m^3}\)

Calculate the change in volume

Finally, we can calculate the change in volume as a result of the heating process as the difference between the final and initial volumes: \(\Delta V = V_2 - V_1 = 0.03924\, \mathrm{m^3} - 0.01929\, \mathrm{m^3} = 0.01995\, \mathrm{m^3}\) The change in volume of the device as a result of the heating is 0.01995 m³.