LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
7 views
in Physics by (110k points)
closed by
At what temperature, the rms velocity of gas molecules would be double of its value at NTP, if pressure is remaining constant?
1. 819°C 
2. 819 K
3. 846 K
4. 546°C 

1 Answer

0 votes
by (59.9k points)
selected by
 
Best answer
Correct Answer - Option 1 : 819°C 

CONCEPT:

Root mean square (R.M.S.) velocity.

  • we know how to relate temperature and kinetic energy, we can relate temperature to the velocity of gas molecules. Note since these are distributions the values (Ek or velocity) that we are talking about are always averages 

\(E_k = \frac{3}{2}RT\)

\(E_k = \frac{1}{2}mv^{2}\)

  • setting these two equal and solving for the average square velocity we get.

\(v^{2} = \frac{3RT}{m}\)

  • The root mean square velocity or Vrms is the square root of the average square velocity and is

\(R.M.S = \sqrt{\frac{3RT}{M}}\)

where R = gas constant, T = temperature (in K), M = molar mass of the gas

​​EXPLANATIONS:

  • From the gas equation, we know

\(c = \sqrt{\frac{3RT}{m}}\)

  • In given condition, 

\(\frac{C_T}{C_o}= \sqrt{\frac{T}{T_o}} => \frac{2C_o}{C_o} = \sqrt{\frac{T}{T_o}}\)

\(=> 4 = \frac{T}{T_o}\)

\(=>T = 4T_o = 4 \times 273 = 1092K = 819^0 C\)

  • hence option 1 is the correct answer.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...