... As shown in the figure, a rigid cylinder is divided into two rooms by a pist

Question

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As shown in the figure, a rigid cylinder is divided into two rooms by a piston that is free to move without gas leakage from one side to another, the left room contains 6 Kg of gas #1 which its initial internal energy(u1left =250 KJ/Kg ) is stirred by a paddle wheel and receives an .amount of work equal to 20 KJ Whereas, the right room contains 4 Kg of gas #2 which experiences compression because of piston motion from left to right and heat rejection equal to 90 KJ. Therefore its (internal energy increases by (delta u right = 50 KJ/Kg : determine .The work done on the piston during its motion (1 the final internal energy (u2left (2

Explanation / Answer

For left portion: Q_left - W_left = m_left*(u2_left - u1_left)

Q_left - (-20 + W_left) = 6*(u2_left - 250)

For right portion: Q_right - W_right = m_right*(u2_right - u1_right)

-90 - W_right = 4*50

W_right = -290 kJ

1) Work done on piston = 290 kJ

2)

Q_left - (-20 + W_left) = 6*(u2_left - 250)

0 - (-20 + 290) = 6*(u2_left - 250)

u2_left = 205 kJ/kg

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