Ncert Exercises & Solutions

Consider a heat engine as shown in the figure. $Q_{1} and Q_{2}$ $Q_{1} and Q_{2}$ are heat added to $T_{1}$ $T_{1}$ and heat taken from $T_{2}$ $T_{2}$ respectively, in one cycle of the engine. W is the mechanical work done on the engine.

If W > 0, then possibilities are:

$(a) Q_{1} > Q_{2} > 0 (b) Q_{2} > Q_{1} > 0 (c) Q_{2} < Q_{1} < 0 (d) Q_{1} < 0, Q_{2} > 0$ $(a) Q_{1} > Q_{2} > 0 (b) Q_{2} > Q_{1} > 0 (c) Q_{2} < Q_{1} < 0 (d) Q_{1} < 0, Q_{2} > 0$

Choose the correct alternatives:
1. (b, c)

2. (a, d)

3. (b, d)

4. (a, c)

(4) Hint: Use the concept of heat engine.

Step 1: Find the relation between W,

Q_{1} and Q_{2}

$Q_{1} and Q_{2}$ .

Considering the figure, we can write,

Q_{1} = W + Q_{2}

$Q_{1} = W + Q_{2}$

\Rightarrow W = Q_{1} - Q_{2} > 0

$\Rightarrow W = Q_{1} - Q_{2} > 0$ (By question)

\Rightarrow Q_{1} > Q_{2} > 0

$\Rightarrow Q_{1} > Q_{2} > 0$ (If both

Q_{1} and Q_{2}

$Q_{1} and Q_{2}$ are positive)

We can also, write

Q_{2} < Q_{1} < 0

$Q_{2} < Q_{1} < 0$ (If both

Q_{1} and Q_{2}

$Q_{1} and Q_{2}$ are negative)

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