Second Law of Thermodynamics

A flask containing $1 \mathrm{mol} {\mathrm{N}}_2$ at $4 \mathrm{atm}$. and $298 \mathrm{K}$ was connected to a flask containing $1 \mathrm{mol}$ ${\mathrm{N}}_2$ gas at $2 \mathrm{atm}$ and $298 \mathrm{K}$. The gases were allowed to mix isothermally, determine the entropy change for the system:

In an experiment, $1\mathrm{kg}$ of water, initially at $283\mathrm{K}$ is heated to $363\mathrm{K}$ via two processes. In process I, water is brought into contact with a heat reservoir at $363\mathrm{K}$. In process II, water is first brought into contact with a heat reservoir at $323\mathrm{K}$ and then in contact with another reservoir at $363\mathrm{K}$. Assume that the specific heat capacity of water, $C$ is independent of temperature. Choose the correct options from the following. (Note $\ln \left(363\right)=5.8944; \ln \left(323\right)=5.7777; \ln \left(283\right)=5.6454$)

An ice cube of mass $30 \mathrm{g}$ at $0^0\mathrm{C}$ is left sitting on the kitchen table where it gradually melts and reaches the kitchen temperature of ${25}^0\mathrm{C}$. The latent heat of fusion for ice is $333 \mathrm{J}·{\mathrm{g}}^{-1}$ and the specific heat of water is $4.2 \mathrm{J}·{\mathrm{g}}^{-1}·{\mathrm{K}}^{-1}$. Select the correct statement(s) about this process. (All numerical values in the answers are rounded to the closest integer.)

Two solid blocks at temperatures $T_1$ and $T_2\left(T_1<T_2\right)$ are put in thermal contact for a long time inside an insulated container. Choose the correct statement(s).

Heat cannot by itself flow from a body at lower temperature to a body at higher temperature” is a statement or consequence of

Write the statement of second law of thermodynamics

Graphs below show the entropy versus energy $U$ of two systems $1$ and $2$ at constant volume. The initial energies of the systems are indicated by $U_{1, i}$ and $U_{2, i} ,$ respectively. Graphs are drawn to the same scale. The systems are then brought into thermal contact with each other. Assume that, at all times the combined energy of the two systems remains constant. Choose the most appropriate option indicating the energies of the two systems and the total entropy after they achieve the equilibrium.

When $1 \mathrm{kg}$ of ice at $0 °\mathrm{C}$ melts to water at $0 °\mathrm{C}$, the resulting change in its entropy, taking latent heat of ice to be $80 \mathrm{cal} {\mathrm{g}}^{-1}$, is,

The change in entropy when a $30 \mathrm{g}$ ice cube at $-12°\mathrm{C}$ is transformed into water at $100°\mathrm{C}$ $($in $\mathrm{J}/\mathrm{K})$ is

$($Take $\ell \mathrm{n}\left(\frac{273}{261}\right)=0.04; \ell \mathrm{n}\left(\frac{373}{273}\right)=0.312$, ${\mathrm{S}}_{\mathrm{ice}}=2100 \mathrm{J}/\mathrm{kg}-{}^{\circ }\mathrm{C},$$\left.{\mathrm{S}}_{\text{water}}=4200 \mathrm{J}/\mathrm{kg}-{}^{\circ }\mathrm{C}, {\mathrm{L}}_{\mathrm{f}}=3.33\times {10}^5 \mathrm{J}/\mathrm{kg}\right)$

A thermally insulated box is divided by a partition into two compartments, each having volume $V.$ Initially one compartment contains $1$ mole of an ideal gas at temperature $T,$ and the other is evacuated. The partition is then broken, and the gas expands to fill both compartments. Its entropy change is:

Determine the change in entropy $\mathrm{\Delta S}$ (in SI unit) of $100 \mathrm{gm}$ of water when it is heated to the boiling point from room temperature of $\mathrm{T}=300\mathrm{K}$, and it is transformed into vapour at the boiling temperature and atmospheric pressure. It is given that for water: the molar heat capacity $\mathrm{C}=75.4\mathrm{J}/\left(\mathrm{mol}-\mathrm{K}\right)$ ; latent heat of vaporization $:\mathrm{ }\mathrm{L}=2.26 \mathrm{MJ}/\mathrm{kg}$

[Take $\ln \left(1.24\right)=0.217$]

Heat engine is a device in which a system undergoes a _____ process resulting in conversion of heat into work. (cyclic/non-cyclic)

_____ in thermodynamics refers to the situation when macroscopic variables describing the thermodynamic state of a system do not depend on time.

A system undergoes a reversible adiabatic process. The entropy of the system

One mole of an ideal monatomic gas undergoes the following four reversible processes:
Step $1 :$ It is first compressed adiabatically from volume $V_1$ to $1 {\mathrm{m}}^2.$
Step $2 :$ then expanded isothermally to volume $10 {\mathrm{m}}^3$
Step $3 :$ then expanded adiabatically to volume $V_3$
Step $4 :$ then compressed isothermally to volume $V_1.$ If the efficiency of the above cycle is $\frac{3}{4}$ then $V_1$ is

What is the entropy change in $J{K}^{-1}$ during the melting of 27.3 g of ice of $0^{o}C$ ? (Latent heat of fusion of ice = 330 $J{g}^{-1}$ )

Choose the incorrect relation among these

According to the third law of thermodynamics which one of the following quantities for a perfectly crystalline solid is zero at absolute zero?

In the following a statement of Assertion is followed by a statement of Reason.

Assertion: During free expansion of an ideal gas, its entropy increases but work done by the gas is zero.

Reason: During free expansion, volume increases but temperature remains constant.