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The pressure 
and volume 
of an ideal gas are related to the density 
of the gas by the expression
State what is meant by the symbol 
.
Use the expression to show that the mean kinetic energy 
of a gas molecule is given by
where 
is the Boltzmann constant and 
is the thermodynamic temperature.
An ideal gas containing 
of molecules is heated at constant volume. Use the expression in (a)(ii) to show that the thermal energy required to raise the temperature of the gas by 
has a value of 
, where 
is the molar gas constant.
