Estimate the average thermal energy of a helium atom at room temperature `(27 ^@C)`

Estimate the average thermal energy of a helium atom at the temperature on the surface of the Sun (6000 K)

Estimate the average thermal energy of a helium atom the temperature of 10 million kelvin (the typical core temperature in the case of a star)

Find the typical de-Broglie wavelength associated with a He atom in helium gas at room temperatuare (27^@C) and 1 atm pressure and compare it with the mean separation between two atoms under these conditions.

Estimate the average mass density of a sodium atom assuming its size to be about 2.5 overset@A . (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the density of sodium in its crystalline phase : 970 kg m^-3 . Are the two densities of the same order of magnitude ? If so, why ?

Obtain the de-Broglie wavelength associated with thermal neutrons at room temperature (27^@C) . Hence explain why a fast neutron beam needs to be thermalized with the environment before it can be used for neutron diffraction experiments.

A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds to a steady value of 2.8 A. What Is the steady temperature of the heating element If the room temperature is 27.0^@C ? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70 xx 10^-4@C .

What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature ? Surface tension of mercury at that temperature ( 20^@C ) is 4.65xx10^-1 N m^-1 The atmospheric pressure is 1.01xx 10^5Pa . Also give the excess pressure inside the drop.

If the co-efficient of perormance of a refrigerator is 5 and operates at the room temperature (27^@C) , find the temperature inside the refrigerator.

A vessel is filled with an ideal gas at a pressure of 20 atm is at a temperature of 27^@ C . One half of the mass is removed from the vessel and the temperature of the remianing gas is increated to 87^@C . What will be the pressure at this temperature?