Question

A heat engine is involved with exchange of heat of $1915J,-40J,+125J\text{and}-QJ$, during one cycle achieving an efficiency of $50.0$%. The value of $Q$ is

• A. $640\text{J}$
• B. $40\text{J}$
• C. $980\text{J}$
• D. $400\text{J}$

Answer 1

The correct option is C $980\text{J}$

$\text{Efficiency},\eta =\frac{\text{Work done}}{\text{Heat absorbed}}$

$\frac{Q_1+Q_2+Q_3+Q_4}{Q_1+Q_3}=0.5$

$\text{Here},Q_1=1915\text{J},Q_2=-40\text{J}\text{and}{Q}_3=125\text{J}$

$\therefore \frac{1915-40+125+Q_4}{1915+125}=0.5$

$\Rightarrow 1915-40+125+Q_4=1020$
$\Rightarrow Q_4=1020-2000$
$\Rightarrow Q_4=-Q=-980\text{J}\Rightarrow Q=980\text{J}$