If $\mathrm{R}$ is universal gas constant the amount of heat needed to raise the temperature of 2 moles of…
If $\mathrm{R}$ is universal gas constant the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from $273 \mathrm{~K}$ to $373 \mathrm{~K}$ when no work is done is
$150 \mathrm{R}$
$100 \mathrm{R}$
$500 \mathrm{R}$
$300 \mathrm{R}$
Solution
For an ideal gas, the internal energy in only a function of the gas temperature and is a measure of the mean translational kinetic energy of the atoms.
$\Delta \mathrm{Q}=\Delta \mathrm{U}+\Delta \mathrm{Q}=0 \Rightarrow \Delta \mathrm{Q}=\Delta \mathrm{U}=\frac{\mathrm{n}}{2} \mathrm{R} \Delta \mathrm{T}$
When $\mathrm{n}=$ degree of freedom for monoatomic gas i.e $=3$
$=\frac{3}{2} \times 2 \mathrm{R}(373-273)=300 \mathrm{R}$