91Ó°ÊÓ

Calculate the root mean square speed of hydrogen molecules at \(373.15 \mathrm{~K}\).

A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature \(T\). Neglecting all vibrational modes, the total internal energy of the system is (a) \(4 R T\) (b) \(15 R T\) (c) \(9 R T\) (d) \(11 R T\)

What is the value of (a) \(0^{\circ} \mathrm{F}\) in Celsius scale? (b) \(0 \mathrm{~K}\) on Fahrenheit scale?

A pendulum clock of time period 2 s gives the correct time at \(30^{\circ} \mathrm{C}\). The pendulum is made of iron. How many seconds will it lose or gain per day when the temperature falls to \(0^{\circ} \mathrm{C}\) ? \(\alpha_{\mathrm{Fe}}=1.2 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}\).

The average translational kinetic energy of \(\mathrm{O}_{2}\) (molar mass 32 ) molecules at a particular temperature is \(0.048 \mathrm{eV}\). The translational kinetic energy of \(\mathrm{N}_{2}\) (molar mass 28 ) molecules in \(\mathrm{eV}\) at the same temperature is \(\quad\) (a) \(0.0015\) (b) \(0.003\) (c) \(0.048\) (d) \(0.768\)

Five gas molecules chosen at random are found to have speed of \(500,600,700,800\) and \(900 \mathrm{~m} / \mathrm{s}\). Find the rms speed. Is it the same as the average speed?

A vessel is filled with an ideal gas at a pressure of \(20 \mathrm{~atm}\) and is at a temperature of \(27^{\circ} \mathrm{C}\). One-half of the mass is removed from the vessel and the temperature of the remaining gas is increased to \(87^{\circ} \mathrm{C}\). At this temperature, find the pressure of the gas.

At what temperature is the Fahrenheit scale reading equal to (a) twice (b) half of Celsius?

A faulty thermometer reads \(5^{\circ} \mathrm{C}\) in melting ice and \(99^{\circ} \mathrm{C}\) in steam. Find the correct temperature in \({ }^{\circ} \mathrm{F}\) when this faulty thermometer reads \(52^{\circ} \mathrm{C}\).

The average speed of all the molecules in a gas at a given instant is not zero, whereas the average velocity of all the molecules is zero. Explain why?