Refrigerators — Revision Notes

⚡ 30-Second Revision

Purpose: — Transfer heat from cold to hot, requires work.
First Law: — $Q_H = Q_C + W$
COP (General): — $\text{COP} = \frac{Q_C}{W} = \frac{Q_C}{Q_H - Q_C}$
COP (Ideal/Carnot): — $\text{COP}_{\text{Carnot}} = \frac{T_C}{T_H - T_C}$ (Temperatures in Kelvin)
Components: — Evaporator (absorbs $Q_C$), Compressor (work $W$), Condenser (rejects $Q_H$), Expansion Valve (pressure drop).
Key Principle: — Second Law of Thermodynamics (Clausius statement) - non-spontaneous heat transfer requires work.

2-Minute Revision

Refrigerators are devices that move heat from a colder region (inside the fridge) to a warmer region (the surroundings), which is against the natural flow of heat. This non-spontaneous process requires an input of external work, typically electrical energy, to power a compressor.

The core operation involves a refrigerant fluid undergoing a cycle of phase changes and pressure variations. Heat ($Q_C$) is absorbed from the cold space in the evaporator, work ($W$) is done on the refrigerant by the compressor, and a larger amount of heat ($Q_H = Q_C + W$) is rejected to the hot surroundings in the condenser.

The performance is measured by the Coefficient of Performance (COP), defined as the ratio of heat extracted ($Q_C$) to the work input ($W$). For an ideal refrigerator, $\text{COP} = T_C / (T_H - T_C)$, where $T_C$ and $T_H$ are absolute temperatures.

Remember to always convert temperatures to Kelvin for calculations.

5-Minute Revision

A refrigerator is a thermodynamic device designed to maintain a region at a temperature lower than its surroundings by continuously extracting heat from it. This process is non-spontaneous and requires external work input, adhering to the Second Law of Thermodynamics (Clausius statement). The most common mechanism is the vapor compression cycle, involving four key components:

1
Evaporator: — Located inside the cold compartment, it absorbs heat ($Q_C$) from the interior, causing the low-pressure liquid refrigerant to vaporize.
2
Compressor: — Powered by external work ($W$), it compresses the low-pressure vapor into a high-pressure, high-temperature vapor.
3
Condenser: — Located outside, it releases the total heat ($Q_H = Q_C + W$) to the warmer surroundings as the high-pressure vapor condenses back into a liquid.
4
Expansion Valve: — Reduces the pressure and temperature of the liquid refrigerant, preparing it to absorb more heat in the evaporator.

The performance is quantified by the Coefficient of Performance (COP), given by $\text{COP} = Q_C / W$. Since $W = Q_H - Q_C$, we can also write $\text{COP} = Q_C / (Q_H - Q_C)$. For an ideal (Carnot) refrigerator, the maximum possible COP is $\text{COP}_{\text{Carnot}} = T_C / (T_H - T_C)$, where $T_C$ and $T_H$ are the absolute temperatures of the cold and hot reservoirs, respectively.

Always convert temperatures to Kelvin. Note that COP can be greater than 1, unlike efficiency. \n\nWorked Example: An ideal refrigerator maintains a temperature of $0^circ\text{C}$ inside and rejects heat to a room at $25^circ\text{C}$.

Calculate its COP. \nSolution: Convert temperatures to Kelvin: $T_C = 0 + 273 = 273,\text{K}$, $T_H = 25 + 273 = 298,\text{K}$. \n$\text{COP} = T_C / (T_H - T_C) = 273 / (298 - 273) = 273 / 25 = 10.92$.

Prelims Revision Notes

Refrigerators: NEET Quick Recall

1. Definition & Principle:

A refrigerator is a device that transfers heat from a lower temperature reservoir ($T_C$) to a higher temperature reservoir ($T_H$).
This process is non-spontaneous and requires external work input ($W$), as per the Clausius statement of the Second Law of Thermodynamics.
It's essentially a heat engine operating in reverse.

2. First Law of Thermodynamics for Refrigerators:

Heat rejected to the hot reservoir ($Q_H$) is the sum of heat extracted from the cold reservoir ($Q_C$) and the work done on the refrigerator ($W$).
Formula: $Q_H = Q_C + W$

3. Coefficient of Performance (COP):

Measures the effectiveness of a refrigerator.
General formula: $\text{COP} = \frac{\text{Heat extracted from cold reservoir}}{\text{Work input}} = \frac{Q_C}{W}$
Using First Law: $\text{COP} = \frac{Q_C}{Q_H - Q_C}$
Important: — COP is typically greater than 1. It is NOT efficiency.

4. Ideal (Carnot) Refrigerator:

Operates on a reversible Carnot cycle, representing the maximum possible COP.
Formula: $\text{COP}_{\text{Carnot}} = \frac{T_C}{T_H - T_C}$
Crucial: — $T_C$ and $T_H$ must be in absolute temperature (Kelvin). Convert Celsius to Kelvin: $T_K = T_C + 273$.

5. Components of Vapor Compression Cycle:

Evaporator: — Absorbs $Q_C$ from cold space, refrigerant vaporizes (low P, low T).
Compressor: — Does work $W$ on refrigerant, increases P and T (high P, high T vapor).
Condenser: — Rejects $Q_H$ to hot surroundings, refrigerant condenses (high P, high T liquid).
Expansion Valve (or Capillary Tube): — Reduces P and T of refrigerant (low P, low T liquid-vapor mixture).

6. Relationship with Heat Engine & Heat Pump:

Refrigerator and Heat Pump are similar, both require work input to move heat from cold to hot.
Refrigerator's goal: cool cold space ($Q_C$ is desired output).
Heat Pump's goal: heat hot space ($Q_H$ is desired output).
$\text{COP}_{\text{heat pump}} = 1 + \text{COP}_{\text{refrigerator}}$ (for same $T_C, T_H$).

7. Common Mistakes to Avoid:

Not converting temperatures to Kelvin.
Confusing COP with efficiency.
Incorrectly applying $Q_H = Q_C + W$ (e.g., adding $Q_H$ and $W$ to get $Q_C$).
Assuming refrigerators 'create cold' instead of 'removing heat'.

Vyyuha Quick Recall

To remember the components of a refrigerator cycle in order: Every Cool Cat Eats.

Evaporator
Compressor
Condenser
Expansion valve