Question 947: Thermodynamics & KTG

Question

The molecules of a given mass of a gas have r.m.s. velocity of 2000 m s
$$-$$1
at 27
o
C and 1.0 $$ 	imes $$ 10
5
N m
$$-$$2
pressure. When the temperature and pressure of the gas are respectively, 127
o
C and 0.05 $$ 	imes $$ 10
5
N m
$$-$$2
, the r.m.s. velocity of its molecules in m s
$$-$$1
is

Accepted Answer

It is observed that the rms velocity of molecule is directly proportional to temperature, so
$${v_{rms}} \propto \sqrt T $$
$$ \Rightarrow v_{rms}^{'} = {v_{rms}}\sqrt {{{T'} \over T}} $$
Hence, $$v_{rms}^{'} = 200 	imes \sqrt {{{400} \over {300}}}  = 400/\sqrt 3 $$

Answer

$${{100\sqrt 2 } \over 3}$$

Answer

$${{100} \over 3}$$

Answer

$$100\sqrt 2 $$

Answer

$${{400} \over {\sqrt 3 }}$$

Thermodynamics & KTG

The molecules of a given mass of a gas have r.m.s. velocity of 2000 m s $-1 at 27 o C and 1.0 \times 10 5 N m -2 pressure. When the temperature and pressure of the gas are respectively, 127 o C and 0.05 \times 10 5 N m -2 , the r.m.s. velocity of its molecules in m s -$1 is

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