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

Question

The figure shows three identical chambers containing a piston and a spring with spring constantk.

a) Which gas exerts the greater force on the piston?
[1] ideal gas 1 [2] ideal gas 2 [3] both the same [4] need more information
b) Which gas exerts the greater pressure on the piston?
[1] ideal gas 1 [2] ideal gas 2 [3] both the same [4] need more information
c) Which gas has the larger temperature?
[1] ideal gas 1 [2] ideal gas 2 [3] both the same [4] need more information
d) Use the ideal gas law to find an expression for the temperature in terms of the spring constantk, the displacementX, the number of molesn, and the ideal gas constantR
[1]T=kX2/(nR) [2]T=nkX2/(R) [3]T=kX/(n2R) [4] none of these

Note: if you cannot view the figure please refer to the link below:

http://www12.0zz0.com/2012/04/15/02/132039143.gif

The figure shows three identical chambers containing a piston and a spring with spring constantk.

Explanation / Answer

(a) the gas in chamber c exerts greater force. This is so because the spring in c is more compressed that means that the force exerted by the gas in c is greater than b. Thus, [2] is the answer.

(b) c. Since, the area of impact is same is both cases and Pressure = Force/Area, thus pressure is larger in c. Thus, [2] is the answer.

(c) From ideal gas law, PV = nRT, thus T = PV/nR. Here n is same in both a and b cases.
Also, as seen in (b) Pressure in "b" is larger than in "a". We can also see that volume of gas in "b" is larger than in "a", thus T is larger in "b". Thus [2] is the answer.

(d) Let the area of piston be "A", then Volume V = AX. Also, force exerted F = kX.
So the Pressure P = kX/A
Thus, Temperature T = PV/nR = (kX/A)(AX)/nR = kX2/nR, thus [1] is the answer.

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