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,
$\frac{W}{Q_1}=\frac{Q_1-Q_2}{Q_1}$
$\frac{W}{Q_1}=1-\frac{Q_2}{Q_1}$
$\frac{W}{Q_1}=1-\frac{T_2}{T_1}\left(\because \frac{Q_1}{Q_2}=\frac{T_1}{T_2}\right)$
$W=Q_1\left(1-\frac{T_2}{T_1}\right)$
$\therefore W=6\times {\left(10\right)}^4\left(1-\frac{(127+273)}{(227+273)}\right)$
$W=6\times {\left(10\right)}^4\left(1-\frac{400}{500}\right)$
$=6\times 10^4\times \frac{100}{500}$
$=1.2\times 10^{4}J$