A piston cylinder assembly contains a gas under pressure as

A piston cylinder assembly contains a gas under pressure as held down by a force of 1500 N as shown in the figure. The total mass of the piston and shaft is 17.3 kg. and while the gas is heated the specific internal energy of the gas increases by 335 kJkg. Meanwhile, the piston and shaft moves upwards resulting in an increase of 0.12 kJ of their potential energy. The piston and cylinder are poor conductors and there is negligible friction between them. Given an atmospheric pressure of 1 aim and gravity equal to 9.807 m/s^2: Write the conservation of mass equation for the gas inside the cylinder. Draw the force balance and determine the pressure of the gas initially in [atm] before heating. If the pressure, volume, and temperature of the gas are related by the following equation, what is the mass in the cylinder initially in |gm]?pV - mRF with the initial volume equal to 0.01 m\\ R -300 J (kg K). and T- 300 KL What would be the final mass inside the cylinder in [gm]? What would the final pressure be in [atm|? What is the polytrophic exponent? What is the displacement of the piston during the process in [cm]? What is the work done by the gas on the piston during the heating process in |kJ]? Draw the control volume and solve for the heat transfer that occurs during the heating process in [kJ] What is the final volume in [cm^3] and temperature in [K] if R remains constant? Show all calculations and unit conversions otherwise no points will be given.

Solution

a. mass remains constant.

b.total force acting downwards

= patm x area of cylinder + 1500 + 17.3 x 9.807

= 1.01 x 10^5 x (3.141/4) x (7.7x 10^-2)^2 + 1500 + 17.3 x9.807

= 511.10 +1500 + 169.66

= 2180.76 N

force acting upwards = pgas x (3.141/4) x (7.7x 10^-2)^2 = 2180.76

so, pgas= 4.68 x 10^5 Pa =4.68 atm

c. pv=mrt

so, 4.68 x 10^5 x 0.01 = m x 300 x 300

so, m=0.052 kg =52 g

let us say piston has moved a distance of h

then 17.3 x 9.8 x h = 120

so, h= 0.7078 m

final volume= 0.01 + (3.141/4)(7.7 x 10^-2)^2 x 0.7078 = 0.0135 m^3

specific heat of gas say c

then 335 = c x (tf-300)

so we can get Tf knowing c

then we can substitute in equation

pfvf=mRTf

so pf = 0.052 x 300 x Tf/0.0135

we know in a polytropic process

p1v1^k =p2v2^k

by substituting all the values we can find k, the polytropic constant

work done = (p2v2-p1v1)/(k-1)=