A refrigerator consuming P watts converts 'g' litres of water into ice in 't' minutes at a temperature T .What quantity of heat will be liberated by the refrigerator in a room during this time if the thermal capacity of the refrigerator is neglected? assume the required.

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To determine the quantity of heat liberated by the refrigerator while converting 'g' liters of water into ice in 't' minutes at a temperature T, we can follow a systematic approach. We need to consider the energy balance and the principles of thermodynamics involved in the refrigeration process.

Understanding the Process

When a refrigerator operates, it removes heat from the interior to freeze water into ice. The energy required to convert water into ice is known as the latent heat of fusion. For water, this value is approximately 334 kJ/kg. Therefore, to find the total heat removed from the water, we can use the following formula:

Calculating the Heat Removed

The heat (Q) required to convert 'g' liters of water into ice can be calculated using the formula:

• Q = m * L

Where:

• m = mass of water in kilograms (kg)
• L = latent heat of fusion (334 kJ/kg)

Since 1 liter of water has a mass of approximately 1 kg, 'g' liters of water will have a mass of 'g' kg. Thus, we can rewrite the equation as:

• Q = g * 334 kJ

Heat Liberation in the Room

While the refrigerator is working to freeze the water, it is also expelling heat to the surrounding environment. The heat expelled by the refrigerator can be understood by considering the work done by the refrigerator and the heat absorbed from the water.

The power consumption of the refrigerator is given as P watts. Since power is the rate of energy transfer, the total energy consumed by the refrigerator in 't' minutes can be calculated as:

• Energy consumed = P * t (in seconds)

To convert minutes to seconds, we multiply 't' by 60:

• Energy consumed = P * (t * 60)

Net Heat Released

The total heat liberated into the room (Q_room) can be expressed as the sum of the heat removed from the water and the energy consumed by the refrigerator:

• Q_room = Q + Energy consumed

Substituting the values we calculated earlier, we get:

• Q_room = (g * 334 kJ) + (P * (t * 60))

Final Expression

In summary, the total quantity of heat liberated by the refrigerator into the room during the time 't' while converting 'g' liters of water into ice at temperature T is:

• Q_room = (g * 334 kJ) + (P * (t * 60))

This formula allows you to calculate the heat released based on the mass of water, the power consumption of the refrigerator, and the time it operates. By plugging in the values for 'g', 'P', and 't', you can find the total heat liberated into the room.

To determine the quantity of heat liberated by the refrigerator while it converts 'g' liters of water into ice in 't' minutes, we need to consider the energy balance involved in the process. The refrigerator operates by removing heat from the water to freeze it, and in doing so, it releases an equivalent amount of heat into the surrounding environment. Let's break this down step by step.

Understanding the Freezing Process

When water freezes, it undergoes a phase change from liquid to solid. This process requires a specific amount of energy, known as the latent heat of fusion. For water, the latent heat of fusion is approximately 334 kJ/kg. This means that to freeze 1 kg of water, 334 kJ of energy must be removed.

Calculating the Mass of Water

First, we need to convert the volume of water (in liters) to mass (in kilograms). The density of water is about 1 kg/L, so:

• Mass of water (m) = g liters = g kg

Energy Required for Freezing

Next, we calculate the total energy required to freeze 'g' liters of water:

• Energy required (Q) = m × L
• Where L is the latent heat of fusion (334 kJ/kg).

Substituting the mass:

• Q = g × 334 kJ

Heat Liberation in the Room

As the refrigerator removes this amount of heat from the water to freeze it, it will release the same amount of heat into the room. Therefore, the quantity of heat liberated by the refrigerator into the room during the time 't' is equal to the energy required to freeze the water:

• Heat liberated (Q_liberated) = g × 334 kJ

Time Factor

While the time 't' is mentioned in the problem, it does not directly affect the total heat liberated, as the energy transfer occurs regardless of the duration. However, it is important to note that the refrigerator consumes power 'P' watts (where 1 watt = 1 joule/second) during this time, which indicates how much energy it uses to perform the freezing process.

Final Expression

In summary, the total quantity of heat liberated by the refrigerator into the room while converting 'g' liters of water into ice in 't' minutes is:

• Q_liberated = g × 334 kJ

This equation provides a clear understanding of the relationship between the mass of water being frozen and the heat released into the environment by the refrigerator. By neglecting the thermal capacity of the refrigerator, we simplify the analysis to focus solely on the heat transfer involved in the phase change of water.