Suppose that 31.4 J of heat is added to an ideal gas. The...

Suppose that 31.4 $\mathrm{J}$ of heat is added to an ideal gas. The gas expands at a constant pressure of $1.40 \times 10^{4}$ Pa while changing its volume from $3.00 \times 10^{-4}$ to $8.00 \times 10^{-4} \mathrm{m}^{3}$ . The gas is not monatomic, so the relation $C_{P}=\frac{5}{2} R$ does not apply. (a) Determine the change in the internal energy of the gas. (b) Calculate its molar specific heat capacity $C_{p} .$

Key Concepts

First Law of Thermodynamics

This principle establishes energy conservation in a thermodynamic process by stating that the energy added to a system as heat is equal to the increase in the system’s internal energy plus the work done by the system on its surroundings. It serves as the foundational rule for analyzing energy transfers during processes such as heating and expansion in gases.

Work Done in Constant Pressure Processes

In thermodynamics, when a gas expands at constant pressure, it does work on its environment. This work is calculated as the product of the constant pressure and the change in volume. Understanding this concept is essential to determining how energy is expended in doing mechanical work during expansions or compressions.

Internal Energy Change in an Ideal Gas

For an ideal gas, the change in internal energy is directly related to the change in temperature and is independent of the process path. This concept allows one to relate the heat added, the work done, and the resulting change in internal energy, and it is particularly useful when applying the first law of thermodynamics to thermodynamic processes.

Molar Specific Heat Capacity at Constant Pressure

Molar specific heat capacity at constant pressure (C_p) is defined as the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius (or Kelvin) at constant pressure. It characterizes how a substance absorbs heat during a constant pressure process, especially when the substance does work by expanding, and is distinguished from the specific heat capacity at constant volume (C_v).

Ideal Gas Law

The ideal gas law is a fundamental equation that relates the pressure, volume, temperature, and number of moles of an ideal gas. It provides the necessary framework for determining various properties, such as temperature changes during expansion or compression, and is crucial when transitioning from work and heat calculations to temperature-based quantities like specific heat capacities.

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