Suppose you inhale 0.50 L of air initially at 20^∘ C and 100 kPa pressure. While holding your br

step 1 Since the air is warmed at constant pressure, so the amount of heat flow from body to air will b

Suppose you inhale 0.50 L of air initially at 20^∘ C and 100...

Suppose you inhale $0.50 \mathrm{L}$ of air initially at $20^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$ pressure. While holding your breath, this air is warmed at constant pressure to $37^{\circ} \mathrm{C}$. Treating the air as an ideal diatomic gas, how much heat flows from the body into the air?

Key Concepts

Heat Transfer under Constant Pressure

In thermodynamic processes at constant pressure, the heat transferred to or from a system is directly related to the change in temperature and the molar heat capacity at constant pressure (C_p). The relationship is given by Q = n*C_p*?T, where Q is the heat added, n is the number of moles, and ?T is the change in temperature. This principle is crucial when analyzing processes like warming or cooling of gases under a constant external pressure.

Specific Heat Capacity of a Diatomic Gas

For diatomic gases such as air, specific heat capacities are used to describe how much energy is needed to raise the temperature of the gas. At constant volume, the molar specific heat capacity, C_v, is typically (5/2)R, and at constant pressure, C_p is (7/2)R, where R is the universal gas constant. These values account for the translational and rotational degrees of freedom present in diatomic molecules and are essential for calculating energy exchanges during temperature changes.

Ideal Gas Law

The Ideal Gas Law is a fundamental relation in thermodynamics that connects pressure, volume, temperature, and the number of moles of an ideal gas. It is expressed as PV = nRT. This equation allows one to determine the amount of gas present given the state variables and forms the basis for many calculations involving gaseous systems.

Temperature Conversion

Temperature conversion, particularly from degrees Celsius to Kelvin, is an important step in thermodynamic calculations since the Kelvin scale is the standard unit for temperature in these equations. The conversion is done using the formula T(K) = T(°C) + 273.15. This ensures that absolute temperatures are used in the Ideal Gas Law and other related thermodynamic formulas.

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