Which of the following statement is false? (1) Internal...

Which of the following statement is false? (1) Internal energy of an ideal gas depends only on the temperature. (2) The relation between $\Delta U$ and $\Delta / /$ is $\Delta / l=\Delta U+$ $P \Delta K$ (3) Heat of a reaction at constant pressure is equal to $I f_{\mathrm{k}}-\|_{\mathrm{p}}$ (4) Heats of reaction at constunt pressure $(\triangle / f)$ and at constant volume $(\Delta U)$ are related as $\Delta / /-\Delta U=$ $\Delta n R T$

Which of the following statement is false?
(1) Internal energy of an ideal gas depends only on the temperature.
(2) The relation between $\Delta U$ and $\Delta / /$ is $\Delta / l=\Delta U+$ $P \Delta K$
(3) Heat of a reaction at constant pressure is equal to $I f_{\mathrm{k}}-\|_{\mathrm{p}}$
(4) Heats of reaction at constunt pressure $(\triangle / f)$ and at constant volume $(\Delta U)$ are related as $\Delta / /-\Delta U=$ $\Delta n R T$

Key Concepts

Internal Energy of Ideal Gases

In thermodynamics, the internal energy of an ideal gas is a state function that depends solely on the temperature of the gas. This property follows from the kinetic theory of gases, where the energy is associated exclusively with the random motion of molecules; thus, variations in pressure or volume in an ideal gas do not affect its internal energy as long as the temperature remains constant.

First Law of Thermodynamics

The First Law of Thermodynamics establishes the conservation of energy principle, stating that energy can neither be created nor destroyed, only transformed. It provides the framework for relating changes in internal energy to the work performed by or on the system and the heat added to or removed from the system. This concept is fundamental in understanding how energy transfers occur during thermodynamic processes.

Enthalpy

Enthalpy is a thermodynamic state function defined as H = U + PV, where U represents internal energy, P is pressure, and V is volume. It is particularly useful in processes occurring at constant pressure, as the heat exchanged under these conditions is equal to the change in enthalpy. This makes enthalpy a central quantity in studying and calculating heat flows in many chemical reactions and phase transitions.

Relationship Between Constant Pressure and Constant Volume Processes

When analyzing thermodynamic processes, especially in chemical reactions, it is important to distinguish between properties measured at constant pressure and constant volume. The difference between the reaction heat measured at constant pressure (which is equivalent to the enthalpy change) and the heat measured at constant volume (the change in internal energy) arises due to the work done by system expansion or contraction. This relationship is often expressed by the term ?nRT, where ?n is the change in the number of moles of gas, R is the gas constant, and T is the temperature, highlighting how molecular changes impact energy balances in chemical reactions.

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