Q59 / 75 · JEE Main 2020 (02 Sep Shift 2) · Physics

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

A
$640 J$
B
$40 J$
Correct answer
C
$980 J$
D
$400 J$

Solution

$I^{st}$ case when $Q_{4}$ is negative $η = \frac{W}{Σ Q_{+}} = \frac{Q_{1} + Q_{2} + Q_{3} + Q_{4}}{Q_{1} + Q_{3}} = 0.5$
$\Rightarrow \frac{1915 - 40 + 125 + Q_{4}}{1915 + 125} = 0.5$
$\Rightarrow 1915 - 40 + 125 + Q_{4} = 1020$
$\Rightarrow Q_{4} = 1020 - 2000 \Rightarrow Q_{4} = - Q = - 980 J$

$Q = 980 J$

${II}^{nd}$ case when $Q_{4}$ $\frac{W}{Σ Q_{+}} = \frac{Q_{1} + Q_{2} + Q_{3} + Q_{4}}{Q_{1} + Q_{3} + Q_{4}} = 0.5$ is positive
$Q_{4} = - 1960$

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

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A heat engine is involved with exchange of heat of 1915 J, –40 J, +125 J and –Q J, during one cycle achieving and efficiency of 50.0%. The value of Q is:

Solution

Relevant Questions

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