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![[Post New]](/templates/default/images/icon_minipost_new.gif) 3 Nov 2007 13:56:14 IST
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An ideal monoatomic gas is confined by a spring loaded massless piston of cross section 8*10-3 m2. Initially the gas is at 300 K and occupies a volume of 2.4*10-3 m3 and the spring is in its relaxed state. The gas is heated by an electric heater until the piston moves out slowly without friction by 0.1 m. Calculate: (a) The final temperature of the gas and (b) the heat supplied by the heater. The force constant of the spring is 800 N/m, atm pressure is 1.0 * 105 N/m2. The cylinder and the piston are thermally insulated.
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4 Nov 2007 11:57:47 IST
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experts please help
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<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
<TR><TD>
<DIV ALIGN="right">Animated Letters</DIV></TD></TR></TABLE>
I am only one,
But still I am one.
I cannot do everything,
But still I can do something;
And because I cannot do everything
I will not refuse to do the something that I can do.
- Edward Everett Hale
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4 Nov 2007 12:30:51 IST
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wait commited an error , solving again
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The heights which great men reached and kept, Were not attained by sudden flight, They, whilst their companions slept, Were toiling upwards in the night.... |
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5 Nov 2007 18:54:31 IST
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Initially the pressure inside cylinder, P0 = 1.01x105 Pa, V0 = 2.4x10-3 and T0 = 300 K
Increase in volume = (area of cross-section).(height by which piston rises) = (8x10-3)(0.1) = 0.0008 m3
So, final volume, V = 0.008+0.0008 = 0.0088 m3
The spring is compressed by 0.1 m and hence it will exert a pressure of kx/A on piston.
So final pressure, P = (P0 + kx/A) = (1.01x105 + 800x0.1/8x10-3) = 1.11x105 Pa
Now apply P0V0/T0 = PV/T
So you can calculate final temperature T from this.
Small work done by gas, dW = P.dV
dW = (P0 + kx/A).d(Ax) = A(P0 + kx/A).dx = (P0A + kx).dx
dQ = dU + dW
Integrate both sides :
Q =  U + [ ] [ ] dW
Q = nCvT + [0] [0.1] (P0A + kx).dx
Now its simple carry out the integration and put the other values to find the heat supplied.
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Bipin Kumar Dubey
Chemical Dept.
IIT Kharagpur
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7 Nov 2007 13:10:00 IST
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well i did the same thing but got answer different from the book's. probably d c pandey solved it wrongly
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<DIV ALIGN="right">Animated Letters</DIV></TD></TR></TABLE>
I am only one,
But still I am one.
I cannot do everything,
But still I can do something;
And because I cannot do everything
I will not refuse to do the something that I can do.
- Edward Everett Hale
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