COMEDK 2023 Shift 1 Paper

To find the root mean square speed (vrms) of the molecules at a different temperature and pressure, we can use the relations from the kinetic theory of gases. For a given mass of gas, the root mean square speed is directly proportional to the square root of the absolute temperature (T) and inversely proportional to the square root of the pressure (P), keeping in mind that the amount of gas does not change. Mathematically, this relationship can be expressed as:
vrms∝√‌

T

P

Given that the initial vrms is 120m∕ s at 88∘C (or 361K, since TK=T‌∘C+273 ) and 1 atmospheric pressure, and we want to find the vrms at 127∘C (or 400K ) and 2 atmospheric pressures, we can set up the following proportion :
‌

vrms,1

vrms,2

=√‌

T1∕P1

T2∕P2

Using the given data:
‌120∕vrms,2=√‌

361∕1

400∕2

‌vrms,2=120×√‌

400∕2

361∕1

‌vrms,2=120×√‌

400

2×361

‌vrms,2=120×√‌

400

722

‌vrms,2=120×√‌

2

1.805

‌vrms,2=120×√1.107694
‌vrms,2≈120×1.052
‌vrms,2≈126.24m∕ s
Hence, the correct answer is Option C: 126.3m∕ s.