Heat given

Question

Carbon monoxide is carried around a closed cycle abc, in which bc is an isothermal process, as shown in the figure. The gas absorbs 7000 J of heat, as its temperature is increased from 300K to 1000K in going from a to b. The quantity of heat rejected by the gas during the process ca is

Moderate

Solution

From a to b heat absorbed = ${\mathrm{nc}}_{\mathrm{v}}\mathrm{dt}$

$\frac{\mathrm{n}5\mathrm{R}}{2}\left(1000-300\right)=7000$

$\frac{\mathrm{n}5\mathrm{R}}{2}\times \left(700\right)=7000$

nR = 4

In the process c to a at constant pressure temperature decreases from 1000 to 300 K.

Heat rejected ${\mathrm{nc}}_{\mathrm{p}}\mathrm{dt}$

$\mathrm{n}\frac{7\mathrm{R}}{2}\left(700\right)$

$\frac{\mathrm{nR}}{2}\times 7\times 700$

$\frac{4}{2}\times 4900=9800\mathrm{J}$

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