Q149 / 200 · Manipal (MET) 2012 · Physics

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

  • A
    $1.6 \times 10^4 \mathrm{~J}$
  • Correct answer
    B
    $1.2 \times 10^4 \mathrm{~J}$
  • C
    $4.8 \times 10^4 \mathrm{~J}$
  • D
    $3.5 \times 10^4 \mathrm{~J}$

Solution

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

Hence, the correct answer is option: 'B'.

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