Question

An ideal gas heat engine operates on a Carnot's cycle between $227^\circ C$ and $127^\circ C$ . It absorbs $6\times 10^{4}J$ at the higher temperature. The amount of heat converted into work is

• A. $1.6\times 10^{4 \, }J$
• B. $1.2\times 10^{4 \, }J$
• C. $4.8\times 10^{4 \, }J$
• D. $3.5\times 10^{4 \, }J$

Answer 1

Answer: (B)

Using the relation,
$\frac{W}{Q_{1}}=\frac{Q_{1} - Q_{2} \, }{Q_{1}}$
$\frac{W}{Q_{1}}=1-\frac{Q_{2}}{Q_{1}}$
$\frac{W}{Q_{1}}=1-\frac{T_{2}}{T_{1}} \, \left(\because \frac{Q_{1}}{Q_{2}} = \frac{T_{1}}{T_{2}}\right)$
$W=Q_{1}\left(1 - \frac{T_{2}}{T_{1}}\right)$
$\therefore \, W=6\times \left(10\right)^{4}\left(1 - \frac{\left(\right. 127 + 273 \left.\right)}{\left(\right. 227 + 273 \left.\right)}\right)$
$W=6\times \left(10\right)^{4}\left(1 - \frac{400}{500}\right)$
$ \, \, =6\times 10^{4}\times \frac{100}{500}$
$ \, \, =1.2\times 10^{4} \, J$