The figure shows three identical chambers containing a piston and a spring whose

Question

The figure shows three identical chambers containing a piston and a spring whose spring constant is k = 5.8 x 104 N/m. The chamber in part (a) is completely evacuated and the piston just touches its left end. In this position, the spring is relaxed. In part (b), 0.75 mol of ideal gas 1 is introduced into the chamber, and the spring compresses by x1 = 15 cm. In part (c), 0.75 mol of ideal gas 2 is introduced into the chamber, and the spring compresses by x2 = 24 cm. Find the temperature of each gas.

Explanation / Answer

Force,

For 1st gas,

F1 = K*x = 5.8*10^4*0.15 = 8700 N,

F1= P1*r^2 = 8700

P1= 8700/r^2

P1*V1 = n1*R*T1

8700/r^2 * x*r^2 = 0.75*8.314*T1

8700 * 0.15= 0.75*8.314*T1

T1 = 209.29 K

For 2nd gas,

F1 = K*x = 5.8*10^4*0.24 = 13920 N

F2= P2*r^2 = 1392

P1= 1392/r^2

P1*V1 = n1*R*T1

13920/r^2 * x*r^2 = 0.75*8.314*T1

13920 * 0.24= 0.75*8.314*T1

T1 = 535.77 K

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