Question

An ideal gas heat engine operates in a Carnot's cycle between ${227}^o$C and ${127}^o$C. It absorbs $6\times {10}^4$J at high 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)

$1.2\times {10}^4$J

Using the relation
$\frac{W}{Q_1}=\frac{Q_1-Q_2}{Q_1}$
or $\frac{W}{Q_1}=1-\frac{Q_2}{Q_1}$
or $\frac{W}{Q_1}=1-\frac{T_2}{T_1}$ $(\therefore \frac{Q_1}{Q_2}=\frac{T_1}{T_2})$
or $W=Q_1\left(1-\frac{T_2}{T_1}\right)$
$\therefore W=6\times {10}^4[1-\frac{127+273}{227+273}]$
or $W=6\times {10}^4\left(1-\frac{400}{500}\right)$
$=6\times {10}^4\times \frac{100}{500}$
$=1.2\times {10}^4$J.