When a monatomic gas expands at constant pressure, the percentages of heat supplied that is used to do…
When a monatomic gas expands at constant pressure, the percentages of heat supplied that is used to do external work and to increase its internal energy are respectively
40,60
25,75
60,40
75,25
Solution
For mono atomic, $\mathrm{n}=3$
$\mathrm{C}_{\mathrm{p}}=\frac{5}{2} \mathrm{R}, \mathrm{C}_{\mathrm{v}}=\frac{3}{2} \mathrm{R}$
Total heat supplied to system, $\mathrm{Q}=\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{T}$
$=\frac{5 \mathrm{nR} \Delta \mathrm{T}}{2}$
Heat needed to increase the internal energy,
$\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}=\frac{3}{2} \mathrm{nR} \Delta \mathrm{T}$
Percentage heat to increase its internal ene: gy
$=\frac{\Delta \mathrm{U}}{\mathrm{Q}} \times 100=\frac{\frac{3}{2} \mathrm{nR} \Delta \mathrm{T}}{\frac{5}{2} \mathrm{nR} \Delta \mathrm{T}} \times 100=60 \%$
Heat required for expansion, $\mathrm{W}=\mathrm{P} \Delta \mathrm{V}$ $=\mathrm{nR} \Delta \mathrm{T}$
Percentage heat to do external work $=\frac{\mathrm{W}}{\mathrm{Q}} \times 100$ $=\frac{\mathrm{nR} \Delta \mathrm{T}}{\frac{5}{2} \mathrm{nR} \Delta \mathrm{T}} \times 100=40 \%$