Question

A frictionless piston-cylinder device contains air at 300 K and 1 bar and is heated until its volume doubles and the temperature reaches 600 K. Answer the following: A. You are interested in studying the air in the piston-cylinder device as a closed system. Draw a schematic of your device and the boundary that defines your system. Assume the cylinder is in horizontal position. B. Determine the final pressure of the air at the end of the process, in bar. Hint: use the ideal gas law equation. If you need the value for the universal gas constant ???????? ????in your textbook or in a chemistry book (or on-line). Just make sure your units are dimensionally correct. C. On a different occasion (different temperature and pressure), you find the piston-cylinder device contains 0.5 kmol of H2O occupying a volume of 0.009 m3. Determine the weight of the H2O in N. Hint: Start with the relationship between number of moles, molecular mass and mass. D. Determine the specific volume of the H2O (from Part C) in m3/kg.

Answer 1

A. Draw a schematic of the system with a boundary around the piston-cylinder device. B. The final pressure can be determined using the ideal gas law equation. C. The weight of H2O can be calculated using the relationship between moles, molecular mass, and mass. D. The specific volume of H2O can be determined by dividing the volume by the mass.

Step-by-step explanation:

A. To study the air in the piston-cylinder device as a closed system, we consider the device itself as the system and draw a boundary around it, including the air inside and excluding the surroundings. The schematic would show a cylindrical container with a piston separating the initial and final air volumes.

B. To determine the final pressure of the air, we can use the ideal gas law. The equation is PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature. Since the volume doubles and the temperature increases to 600 K, we can set up the equation (1 bar)(2V) = n(R)(600 K), and solve for the final pressure.

C. To determine the weight of H2O in the piston-cylinder device, we use the relationship between number of moles, molecular mass, and mass. The weight of H2O in N can be calculated as (0.5 kmol)(molecular mass of H2O)(Acceleration due to gravity).

D. The specific volume of H2O can be determined by dividing the volume (0.009 m3) by the mass of H2O (which we can calculate from the number of moles and molecular mass).

Answer 2

Part a: The schematic diagram is attached.

Part b: The pressure at the end is 1 bar.

Part c: Weight of 0.5kmol of water is 88.2 N.

Part d: The specific volume is 0.001 m^3/kg

Step-by-step explanation:

Part a

The schematic is given in the diagram attached.

Part b

Pressure is given using the ideal gas equation as

Here

• P_1=1 bar
• P_2=? to be calculated
• V_2=2V_1
• T_1=300K
• T_2=600K

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)\\(1* V_1)/(300)=(P_2* 2V_1)/(600)\\P_2=(600)/(600)\\P_2=1 bar`

So the pressure at the end is 1 bar.

Part c

Mass of 0.5kmol is given as follows

`Mass=n_(moles) * Molar \, Mass\\Mass=0.5 * 10^3 * 18 * 10^(-3)\\Mass=9.0 kg`

Weight is given as

`W=mxg\\W=9 * 9.8\\W=88.2 \, N`

So weight of 0.5kmol of water is 88.2 N.

Part d

Specific volume is given as

`v=(Volume)/(Mass)\\v=(0.009)/(9)\\v=0.001 m^3/kg`

So the specific volume is 0.001 m^3/kg