Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Medical
  • One mole of oxygen at is inclosed in a vessel which is thermally insu

One mole of oxygen at 27^{\circ} \mathrm{C} is inclosed in a vessel which is thermally insulated. The vessel is moved with a constant speed v and is then suddenly stopped. The process results in a rise of temperature of the gas by 1^{\circ} \mathrm{C}. Then, if M = Molecular mass of oxygen

Option: 1

\mathrm{\gamma\left(=C_p / C_v\right)=\frac{5}{3}}


Option: 2

\mathrm{\gamma=\frac{8}{5}}


Option: 3

\mathrm{v=\sqrt{\frac{R}{M(\gamma+1)}}}


Option: 4

\mathrm{v=\sqrt{\frac{2 R}{M(\gamma-1)}}}


Answers (1)

best_answer

Oxygen is diatomic; it has 5 degrees of freedom. Therefore,\mathrm{C_v=5 R / 2 \text { and } C_p=7 R / 2}. So\mathrm{\gamma=C_p / C_v=7 / 5}. The kinetic energy of oxygen molecules with a velocity \mathrm{v_0=\frac{1}{2} M v^2}, where M = molecular weight of oxygen

\mathrm{\text { Now heat energy }=C_v d T=C_v \times 1=C_v}

\mathrm{\begin{aligned} & \text { But } C_p-C_v=R \text { or } \frac{C_p}{C_v}-1=\frac{R}{C_v} \\ & \operatorname{Or}(\gamma-1)=\frac{R}{C_v} \text { or } C_v=\frac{R}{(\gamma-1)} \end{aligned}}

\mathrm{\text { Therefore, } \frac{1}{2} M v^2=\frac{R}{(\gamma-1)}}

\mathrm{\operatorname{Or} v=\sqrt{\frac{2 R}{M(\gamma-1)}}}

So the correct choices are (b) and (d)

Posted by

Gunjita

View full answer

NEET 2024 Most scoring concepts

    Just Study 32% of the NEET syllabus and Score up to 100% marks

Similar Questions

Trending Articles/News

anam-khan

NEET UG 2026 Paper Leak: Biology lecturer, part of NTA's paper-setting committee for NEET, arrested
anam-khan

NEET Paper Leak: Student dies by suicide in Rajasthan’s Sikar amid controversy
anam-khan

NTA opens NEET UG 2026 re-exam correction window to modify address, select choice of cities

Latest Question