A room in a well-insulated building has a volume of 120 m^3. The air in the room is at 21^∘ C.

step 1 In this question we have given a cylindrical tube and in this there are two frictionless piston

A room in a well-insulated building has a volume of 120...

A room in a well-insulated building has a volume of $120 \mathrm{~m}^3$. The air in the room is at $21^{\circ} \mathrm{C}$. How much heat must be added to the air in order to increase its temperature by $1^{\circ} \mathrm{C}$ ?

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Key Concepts

Specific Heat Capacity

This is the property of a material that indicates the amount of heat required to raise the temperature of a unit mass of the substance by one degree Celsius. In thermodynamics, it is essential for calculating how much energy is needed to achieve a desired temperature change in a substance, such as air in a room.

Mass Calculation from Density and Volume

In many practical problems, such as calculating the heat required to warm a room, the mass of the air is determined by multiplying the volume of the space by the density of air. This concept allows one to convert volumetric information into mass, which is necessary when applying the specific heat capacity to energy calculations.

Energy Balance Equation (Q = m c ?T)

This fundamental relationship in thermodynamics links the amount of heat added (Q) to the mass (m), the specific heat capacity (c), and the change in temperature (?T) of a system. It provides a straightforward method to compute the heat energy required for a specified temperature increase, which is critical in designing heating or cooling processes.

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