[Adapted from Endem (1938)] It is desired to heat a room at...

[Adapted from Endem (1938)] It is desired to heat a room at initial temperature $10^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$. The volume of the room is $20 \mathrm{~m}^3$ and the initial pressure is 1 atm. The molar constant-volume heat capacity for air is $3.6 R$. (i) Suppose first that there is no heat loss nor movement of air in or out of the room. Determine the heat input required to warm the room. (ii) Now suppose air moves out of the room during the heating, such that the pressure remains constant. Show that in this case the energy of the air remaining in the room at the end is the same as that of the energy of the air in the room at the beginning. (iii) Explain where the energy supplied as heat has gone, and calculate how much heat was supplied.

[Adapted from Endem (1938)] It is desired to heat a room at initial temperature $10^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$. The volume of the room is $20 \mathrm{~m}^3$ and the initial pressure is 1 atm. The molar constant-volume heat capacity for air is $3.6 R$.
(i) Suppose first that there is no heat loss nor movement of air in or out of the room. Determine the heat input required to warm the room.
(ii) Now suppose air moves out of the room during the heating, such that the pressure remains constant. Show that in this case the energy of the air remaining in the room at the end is the same as that of the energy of the air in the room at the beginning.
(iii) Explain where the energy supplied as heat has gone, and calculate how much heat was supplied.

Key Concepts

First Law of Thermodynamics

This law states that energy is conserved in any process; the change in internal energy of a system equals the heat added to it minus the work done by the system. This concept is fundamental when analyzing energy transfers during heating processes, whether the system is closed or open, and under constant volume or constant pressure conditions.

Heat Capacity

Heat capacity is a measure of the amount of heat required to change a system’s temperature. In thermodynamics, there is an important distinction between constant-volume heat capacity and constant-pressure heat capacity, which accounts for whether the system performs work during expansion. These concepts help quantify energy changes in different thermodynamic processes.

Constant Volume and Constant Pressure Processes

In a constant volume process, the system's volume remains fixed during heating, meaning no work is done by expansion and all the heat contributes directly to increasing the internal energy. In contrast, a constant pressure process allows the system to expand, so part of the supplied heat is used for doing work, affecting the net energy change in the system.

Energy Conservation in Open and Closed Systems

Energy conservation principles differ depending on whether the system is closed (with no mass exchange) or open (where mass, and thus energy, can be exchanged with the surroundings). In open systems under constant pressure, energy can leave with the mass that exits, even if the remaining system appears to have unchanged internal energy.

Work in Thermodynamic Processes

Work refers to energy transfer as a result of volume changes under external pressure. In thermodynamic processes, especially under constant pressure, calculating the work done is essential as it accounts for the energy used in expanding the system, thereby influencing how the added heat is partitioned between increasing internal energy and performing mechanical work.

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