Consider a vertical piston-cylinder assembly with a 50 kg piston attached to a s
ID: 1939939 • Letter: C
Question
Consider a vertical piston-cylinder assembly with a 50 kg piston attached to a spring and exposed to atmospheric pressure of 100 kPa. The piston has a surface area of 250 cm^2 and the local acceleration of gravity is 9.81 m/s^2. Heat is now transferred to the system causing it to expand until the volume is 50% greater than the initial volume and reaches 0.003m^3, at which the state pressure in the cylinder is 2 bar. During the process, the spring exerts a force that varies linearly from an initial value of 0 N to a final value. Neglect friction between the piston and the cylinder.2. Find the spring constant
Explanation / Answer
work done=work by piston+by atmospheric pressure =F*dx +Pdv=-50*9.81*(.003/2)/(250*10^-4)-100*10^3*(.003/2)=-179.43Joules spring P=Kx When P=2 bar=2*101.325kpa x=.oo3 m^3 So K=6.755*10^7 Therefore work done =integral of kxdx=Kx^2/2 from x=.oo3/2 to x=.003 =227.98Joule