Question

Consider a heat engine as shown in figure Q₁ and Q₂ are heat added to heat bath T₁ and heat taken from T₂ in one cycle of engine. W is the mechanical work done on the engine. If W > 0, then possibilities are ______.

1. Q₁ > Q₂ > 0
2. Q₂ > Q₁ > 0
3. Q₂ < Q₁ < 0
4. Q₁ < 0, Q₂ > 0

Answer 1

Refrigerator or Heat Pump: A refrigerator or heat pump is basically a heat engine run in the reverse direction. It essentially consists of three parts:

Source: At higher temperatures T₁

Working substance: It is called refrigerant liquid ammonia and freon works as a working substance.

Sink: At lower temperature T₂. The working substance takes heat Q₂ from a sink (contents of the refrigerator) at a lower temperature, has a net amount of work done W on it by an external agent (usual compressor of the refrigerator) and gives out a larger amount of heat Q₁, to a hot body at temperature T₁ (usually atmosphere). Thus, it transfers heat from a cold body to a hot body at the expense of mechanical energy supplied to it by an external agent. The cold body is thus cooled more and more.

We know that the diagram represents the working of a refrigerator. So, we can write

`Q_1 + W + Q_2`

According to the problem, `W > 0`, then

⇒ `W = Q_1 - Q_2 > 0`

So there are two possibilities: 

a. If both `Q_1` and `Q_2` are positive,

⇒ `Q_1 > Q_2 > 0`

c. If both `Q_1` and `Q_2` are positive,

⇒ `Q_2 > Q_1 > 0`