Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Medical
  • The rms speed of the molecules of an ideal gas at STP is 0.5 km/sec. Find the density of the gas. What will be the density at <img alt="21^{^{\cdot }}" src="https://entrancecorner.oncodecogs.c

The rms speed of the molecules of an ideal gas at STP is 0.5 km/sec. Find the density of the gas. What will be the density at 21^{^{\cdot }}C. If pressure remain the same? Give atmospheric pressure=10^{^{\5}}\frac{N}{M^{^{\2}}}

Option: 1

1.11 \mathrm{~kg} \cdot \mathrm{M}^{-3}


Option: 2

1.12 \mathrm{~kg} \cdot \mathrm{M}^{-3}


Option: 3

1.11 \mathrm{~kg}


Option: 4

1.14 \mathrm{~kg}


Answers (1)

best_answer

rms speed,c=\sqrt{\frac{3 P}{P}} ; S_{0} P=\frac{3 P}{c^{2}}

Here,\begin{aligned} & P=10^{5} \mathrm{~N} \cdot \mathrm{M}^{-2} \\ & C=0.5 \mathrm{Km} \cdot \mathrm{S}^{-1}=0.5 \times 1000 \mathrm{M} \cdot \mathrm{S}^{-1}=500 \mathrm{M} \cdot \mathrm{s}^{-1} \\ & \therefore \quad=\frac{3 \times 10^{5}}{(500)^{2}}=1.2 \mathrm{~kg} \cdot \mathrm{M}^{-3} \\ & \therefore \quad \text { also } c \propto \sqrt{T} \text {. So, } \end{aligned}

At constant pressure,c \propto \frac{1}{\sqrt{P}}$; also $c \propto \sqrt{T}, S_{0}, P \propto \frac{1}{T}

Then\frac{P_{0}}{P_{21}}=\frac{T_{21}}{T_{0}}$ or, $P_{21}=P_{0} \frac{T_{0}}{T_{21}}\left[T_{0}=0^{\circ} \mathrm{C}=273 \mathrm{~K}\right.]

\begin{aligned}& \left.T_{21}=21^{\circ} \mathrm{C}=(21+273) \mathrm{K}=294 \mathrm{~kJ}\right] \\ & =1.2 \times \frac{273}{284}=1.11 \mathrm{~kg} \cdot \mathrm{M}^{-3} \end{aligned}

 

Posted by

Gautam harsolia

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 Paper Leak: Court extends CBI custody of accused Manisha Hawaldar by 2 days
anam-khan

'PM Modi personally supervising the situation': Centre tells SC in NEET case
anam-khan

NEET Paper Leak Row: NTA informs SC of security overhaul, institutional reforms

Latest Question