Q.(a) Derive the relation between 'Cp' and 'Cv' for an ideal gas.

Apply the first law of thermodynamics: delta U = q + w, where q is heat given TO the system (positive if absorbed) and w is work done ON the system (negative if the system does work on the surroundings).

Given:

q = +701 J (heat absorbed BY the system, so positive by IUPAC sign convention). …

Internal energy includes translational, rotational, vibrational, electronic and nuclear (bond) energies of a system's particles, but excludes external positional energy such as gravitational potential energy.

The internal energy (U) of a system is the sum of all forms of energy associated with the motion and arrangement of the molecules/atoms that make up the system: kinetic energy from molecular translation, rotation, and vibration, plus potential energy from chemical bonds (which is related to nuclear/electronic energy). These are all energies the system possesses on its own, regardless of its surroundings.

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The first law of thermodynamics is expressed as delta U = q + w -- the change in internal energy equals heat absorbed plus work done on the system.

The first law of thermodynamics (law of conservation of energy) states that energy can neither be created nor destroyed, only converted from one form to another. For a closed system, if q is the heat absorbed by the system and w is the …

Since the number of gas moles decreases in this reaction, ΔH < ΔE.

The relation between enthalpy change and internal energy change is $\Delta H = \Delta E + \Delta n_g RT$, where $\Delta n_g$ = (moles of gaseous products) − (moles of gaseous reactants).

For $CO(g) + \tfrac{1}{2}O_2(g) \rightarrow CO_2(g)$:

$\Delta n_g = 1 - (1 + 0.5) = -0.5$

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The first law of thermodynamics states that the change in internal energy of a system equals the heat added to the system plus the work done on the system: ΔU = q + w.

This is simply energy conservation: any energy that flows into a system, whether as heat (q) or as work done on it (w), must show up as a change in its internal energy (ΔU). None of the other options (ΔU = q×w, ΔU = −q−w, ΔU = …

The first law states energy can neither be created nor destroyed; mathematically ΔU = q + w.

The first law of thermodynamics is a statement of the law of conservation of energy: the change in internal energy of a system equals the heat supplied to it plus the work done on it.

$\Delta U = q + w$

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Endothermic reactions absorb heat, so $\Delta H > 0$ always.

Enthalpy change $\Delta H = H_{products} - H_{reactants}$. In an endothermic reaction, heat is absorbed from the surroundings, meaning the products end up at a higher energy (enthalpy) than the reactants. Hence $H_{products} > H_{reactants}$, which …

Internal energy is the total energy contained in a system due to molecular motion and molecular interactions; it is a state function.

Every system is made up of a very large number of molecules. Internal energy (U) is defined as the sum of the kinetic energy (translational, rotational, vibrational motion of molecules) and the potential energy (arising from intermolecular forces of attraction/repulsion, and chemical bond energy) of all the particles making up the system.

Key points:

• U is an extensive property (depends on the amount of substance) and a state function (depends only on the initial and final state of the system, not on the path followed).
• Only the change in internal energy, ΔU = U_final - U_initial, can be experimentally measured; the absolute value of U cannot be determined. …