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  • An ideal monoatomic gas is confined in a cylinder by spring-loaded position of cross-section <img alt="8.0 \times 10^{-3} \mathrm{~m}^{2}" src="https://entrancecorner.oncodecogs.com/gif.latex?8.0%2

An ideal monoatomic gas is confined in a cylinder by spring-loaded position of cross-section 8.0 \times 10^{-3} \mathrm{~m}^{2} lnitially the gas is at 300 \mathrm{~K} and occupies a volume of 2.4 \times 10^{-3} \mathrm{~m}^{3} and the spring is in its relaxed (unscratched uncompressed) state. The gas is heated by a small electricity heater until the piston moves out slowly by 0.1 \mathrm{~m}. The final temperature of the gas is:
(The force constant of the spring is 8000 \mathrm{~N} / \mathrm{m}, and the atmospheric pressure 10 \times 10^{5} \mathrm{Nm}^{-2}.)

Option: 1

400 \mathrm{~K}


Option: 2

500 \mathrm{~K}


Option: 3

650 \mathrm{~K}


Option: 4

800 \mathrm{~K}


Answers (1)

best_answer

\mathrm{Final \: pressure =\mathrm{P}_{0}+\frac{k x}{A}}
\mathrm{ =1.0 \times 10^{5}+\frac{(8000)(0.1)}{8 \times 10^{-3}}}
\mathrm{ =2 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}}

\mathrm{ Final \: volume =2.4 \times 10^{-3}+(0.1)\left(8 \times 10^{-3}\right)}
\mathrm{ =3.2 \times 10^{-3} \mathrm{~m}^{3}}

\mathrm{ Applying, \frac{P_{i} V_{i}}{T_{i}}=\frac{P_{f} V_{f}}{T_{f}}}
\mathrm{ We \: have, \mathrm{T}_{\mathrm{f}}=\left(\frac{P_{f} V_{f}}{P_{i} V_{i}}\right) \mathrm{T}_{\mathrm{i}}}
\mathrm{ =\frac{\left(2 \times 10^{5}\right)\left(3.2 \times 10^{-3}\right)}{\left(1 \times 10^{5}\right)\left(2.4 \times 10^{-3}\right)} \times 300}
\mathrm{ =800 \mathrm{~K}}
 

 

Posted by

Deependra Verma

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