Basic concepts Questions in English

(A) The enthalpy change is defined as $\Delta H = \Delta E + \Delta(PV)$.
For a system where pressure $(P)$ is constant, the expression becomes $\Delta H = \Delta E + P \Delta V$.
Therefore, the relation is valid under the condition of constant pressure.

(C) $1$. An endothermic process is one that absorbs heat from the surroundings.
$2$. Mixing $NaOH$ and $HCl$ is a neutralization reaction, which is exothermic.
$3$. The $Haber$ process $(N_2 + 3H_2 \rightleftharpoons 2NH_3)$ is exothermic.
$4$. Freezing of water is an exothermic process as it releases latent heat.
$5$. Melting of ice requires the absorption of latent heat from the surroundings, making it an endothermic process.

(B) $1$. The internal energy $\Delta U$ of an ideal gas is a function of temperature only, i.e., $\Delta U = f(T)$.
$2$. For an isothermal process, the temperature remains constant, so $\Delta T = 0$.
$3$. Since $\Delta T = 0$, the change in internal energy $\Delta U$ is equal to $0$.

(C) $1$. The internal energy $(U)$ of an ideal gas is a function of temperature $(T)$ only, i.e., $U = f(T)$.
$2$. In an isothermal process, the temperature of the system remains constant $(dT = 0)$.
$3$. Since the temperature does not change, the internal energy of the system remains constant $(\Delta U = 0)$.
$4$. Therefore, the correct option is $C$.

(A) $1$. Properties that depend on the amount of matter are called extensive properties (e.g., $Heat$, $Enthalpy$, $Entropy$, $Free \ energy$).
$2$. Properties that depend on the path taken are called path functions.
$3$. $Heat$ $(q)$ and $Work$ $(w)$ are path functions, whereas $Free \ energy$, $Enthalpy$, and $Entropy$ are state functions (they depend only on the initial and final states, not the path).
$4$. Since $Heat$ is both an extensive property (depends on the amount of matter) and a path function, it is the correct answer.

(C) $1$. $A$ state function is a property whose value depends only on the current state of the system and not on the path taken to reach that state.
$2$. $Volume$ $(V)$, $Pressure$ $(P)$, and $Temperature$ $(T)$ are state functions because they depend only on the state variables of the system.
$3$. $Work$ $(w)$ and $Heat$ $(q)$ are path functions, meaning their values depend on the process or path taken to change the state of the system.
$4$. Therefore, $Work$ is not a state function.

(D) $1$. In thermodynamics, a process where there is no exchange of heat $(q = 0)$ between the system and the surroundings is defined as an adiabatic process.
$2$. For an adiabatic process, the first law of thermodynamics simplifies to $\Delta U = w$, where $\Delta U$ is the change in internal energy and $w$ is the work done.
$3$. Therefore, the correct option is $D$.

(A) For an isothermal reversible compression of an ideal gas, the work done $W$ is given by the formula:
$W = -nRT \ln\left(\frac{P_1}{P_2}\right)$
Given:
$n = 1 \text{ mol}$
$R = 8.314 \text{ J K}^{-1} \text{mol}^{-1}$
$T = 300 \text{ K}$
$P_1 = x \text{ kPa}$
$P_2 = 2x \text{ kPa}$
Substituting the values:
$W = -(1 \text{ mol}) \times (8.314 \text{ J K}^{-1} \text{mol}^{-1}) \times (300 \text{ K}) \times \ln\left(\frac{x}{2x}\right)$
$W = -2494.2 \times \ln(0.5)$
$W = -2494.2 \times (-0.693)$
$W \approx 1729 \text{ J}$
Since the gas is compressed, work is done on the system, hence the value is positive.

(B) $1$. Internal energy $(U)$ and entropy $(S)$ depend only on the state of the system, not on the path taken to reach that state, hence they are state functions.
$2$. Work $(w)$ and heat $(q)$ are path functions, not state functions.
$3$. Internal energy does not change in an isothermal process for an ideal gas $(\Delta U = 0)$.
$4$. Work done in an adiabatic process is not necessarily zero; it is given by $w = \Delta U$.