In an ideal gas at temperature $$T,$$ the average force that a molecule applies on the walls of a closed container depends on $$T$$ as $${T^q}.$$ A good estimate for $$q$$ is:
A.
$$\frac{1}{2}$$
B.
$$2$$
C.
$$1$$
D.
$$\frac{1}{4}$$
Answer :
$$1$$
Solution :
Pressure, $$P = \frac{1}{3}\frac{{mN}}{V}V_{rms}^2$$
$${\text{or,}}\,\,P = \frac{{\left( {mN} \right)T}}{V}$$
If the gas mass temperature are constant then
$$P \propto {\left( {{V_{rms}}} \right)^2} \propto T$$
$${\text{So,}}\,{\text{force}} \propto {\left( {{V_{rms}}} \right)^2} \propto T$$
i.e., Value of $$q = 1$$
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