An ideal gas initially at P_i, V_i, and T_i is taken through a cycle as in the F

Question

An ideal gas initially at P_i, V_i, and T_i is taken through a cycle as in the Figure. The universal gas constant has a value of 8.314 J/mol middot K. Calculate the net work done on the gas per cycle. What is the net energy added by heat to the system per cycle? Obtain a numerical value for the network done per cycle for 1.00 mol of gas initially at 0 degree C. A block of mass m_1 = 2.00 kg and a block of mass m_2 = 6.00 kg are connected by a string of negligible mass over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. These blocks are allowed to move on a fixed block-wedge of angle 0 = 30.0 degree as shown in the Figure. The coefficient of kinetic friction is 0.360 for both blocks. Draw the free-body diagrams of both blocks and of the pulley. Calculate the acceleration of the two blocks. Calculate the two tensions in the string.

Explanation / Answer

(a). Net wirk done on the gas per cycle W = Area of the square

= AB xAC

=(3Pi-Pi) (3Vi-Vi)

= 2Pi x 2Vi

= 4PiVi

(b).Energy added to the system per cycle Q = Area under BC line and volume axis

= 3Pi (3Vi-Vi)

= 3Pi x2Vi

= 6PiVi

(c).Number of moles n = 1 mol

Temperature Ti = 0 o C = 273 K

We know PiVi = nRTi

=(1)(8.314)(273)

= 2269.722

So, W = 4PiVi

= 4(2269.722)

= 9078.888 J

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