UNIFIED ENGINEERING Fall 2005

Ian A. Waitz

Problem T2. (Unified Thermodynamics)

Consider a massless piston-cylinder arrangement with a spring inside the cylinder. The initial state corresponds to the condition when the piston is 0.2 m from the bottom of the cylinder and the spring is uncompressed, but just touching the bottom of the piston. Both the internal and external pressure are 100 kPa. The temperature of the air in the cylinder is 300K and the temperature of the surroundings is 300K. An external force is slowly applied to compress the spring and the air in the cylinder. The cylinder is not thermally insulated and the process proceeds slowly enough so that the temperature of the air in the cylinder is always 300K. The final state corresponds to the condition where the piston has been displaced 0.1 m (halfway to the bottom of the cylinder).

Piston face diameter= 0.15 m

Spring constant = 2 x 10⁴ N/m

a) Draw this process on a p-v diagram.

b) What is the work done by the air in the cylinder during the compression process?

c) What is the work done by the spring during the compression process?

d) What is the work done by the atmosphere during the compression process?

e) What is the work done by the external force during the compression process?

(Figure taken from Schmidt et al., 2004)

(LO#4, LO#5)