Thermodynamics Questions

Consider the reaction: ${\text{N}}_2(g)+3{\text{H}}_2(g)\to 2{\text{NH}}_3(g)$ carried out at constant temperature and pressure. If $\Delta H$ and $\Delta U$ are the enthalpy and internal energy changes for the reaction, which of the following expressions is true?

One mole of ideal monoatomic gas ($\gamma =5/3$) is mixed with one mole of diatomic gas ($\gamma =7/5$). What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure to that at constant volume.

If the temperature of the sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$, then the ratio of the radiant energy received on earth to what it was previously will be:

Which of the following statements is correct for any thermodynamic system?

Two thermally insulated vessels $1$ and $2$ are filled with air at temperatures $(T_1,T_2)$, volume $(V_1,V_2)$ and pressure $(P_1,P_2)$ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be:

A radiation of energy $E$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is:

The temperature of two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x$ respectively, are $T_2$ and $T_1$ ($T_2>T_1$). The rate of heat transfer through the slab in a steady state is $\frac{A(T_2-T_1)K}{x}f$, where $f$ is:

For a spontaneous reaction the $\Delta G^{\circ }$, equilibrium constant ($K$) and $E_{\text{cell}}^{\circ }$ will be respectively:

If the bond dissociation energies of $\text{XY},{\text{X}}_2$ and ${\text{Y}}_2$ are in the ratio $1:1:0.5$ and ${\Delta }_{f}H$ for $\text{XY}$ is $-200\text{kJ/mol}$, the bond dissociation energy of ${\text{X}}_2$ will be:

A schematic plot of $\ln K_{eq}$ versus inverse of temperature ($1/T$) for a reaction is shown below. The reaction must be:

($\Delta H-\Delta U$) for the formation of carbon monoxide ($\text{CO}$) from its elements at $298\text{K}$ is ($R=8.314{\text{J K}}^{-1}{\text{ mol}}^{-1}$):

An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system. If $T_i$ is the initial temperature and $T_f$ is the final temperature, which of the following statements is correct?

A Carnot engine, having an efficiency of $\eta =1/10$ as a heat engine, is used as a refrigerator. If the work done on the system is $10\text{J}$, the amount of energy absorbed from the reservoir at lower temperature is:

Work of $146\text{kJ}$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $7^{\circ }\text{C}$. The gas is: ($R=8.3{\text{J mol}}^{-1}{\text{K}}^{-1}$)

Assuming the sun to be a spherical body of radius $R$ at a temperature of $T\text{K}$, evaluate the total radiant power incident on Earth at a distance $r$ from the Sun. (where $r_0$ is the radius of the Earth and $\sigma$ is Stefan’s constant).

If $C_p$ and $C_v$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then:

When a system is taken from state $i$ to state $f$ along the path $iaf$, it is found that $Q=50\text{cal}$ and $W=20\text{cal}$. Along the path $ibf$, $Q=36\text{cal}$. $W$ along the path $ibf$ is:

The energies of activation for forward and reverse reactions for $A_2+B_2\rightleftharpoons 2AB$ are $180{\text{kJ mol}}^{-1}$ and $200{\text{kJ mol}}^{-1}$ respectively. The presence of a catalyst lowers the activation energy of both (forward and reverse) reactions by $100{\text{kJ mol}}^{-1}$. The enthalpy change of the reaction ($A_2+B_2\to 2AB$) in the presence of catalyst will be (in ${\text{kJ mol}}^{-1}$):

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $T_0$, while Box B contains one mole of helium at temperature $(7/3)T_0$. The boxes are put into thermal contact. The final temperature $T_f$ is:

Three perfect gases at absolute temperatures $T_1,T_2$ and $T_3$ are mixed. The masses of molecules are $m_1,m_2$ and $m_3$ and the number of molecules are $n_1,n_2$ and $n_3$ respectively. Assuming no loss of energy, the final temperature of the mixture is:

Directions: Question numbers 28, 29 and 30 are based on the following paragraph. Two moles of helium gas are taken over the cycle ABCDA, as shown in the P – T diagram.

Two moles of helium gas are taken over the cycle $ABCDA$, as shown in the $P–T$ diagram. Assuming the gas to be ideal, the work done on the gas in taking it from $A$ to $B$ is:

Referring to the $P–T$ diagram in the previous question, the work done on the gas in taking it from $D$ to $A$ is:

Referring to the $P–T$ diagram, the net work done on the gas in the cycle $ABCDA$ is:

In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is ${\text{CH}}_3\text{OH}(l)+\frac{3}{2}{\text{O}}_2(g)\to {\text{CO}}_2(g)+2{\text{H}}_2\text{O}(l)$. At $298\text{K}$ standard Gibb’s energies of formation for ${\text{CH}}_3\text{OH}(l)$, ${\text{H}}_2\text{O}(l)$ and ${\text{CO}}_2(g)$ are $-166.2$, $-237.2$ and $-394.4{\text{kJ mol}}^{-1}$ respectively. If standard enthalpy of combustion of methanol is $-726{\text{kJ mol}}^{-1}$, efficiency of the fuel cell will be:

The standard enthalpy of formation of ${\text{NH}}_3$ is $-46.0{\text{kJ mol}}^{-1}$. If the enthalpy of formation of ${\text{H}}_2$ from its atoms is $-436{\text{kJ mol}}^{-1}$ and that of ${\text{N}}_2$ is $-712{\text{kJ mol}}^{-1}$, the average bond enthalpy of $\text{N}-\text{H}$ bond in ${\text{NH}}_3$ is:

For a particular reversible reaction at temperature $T$, $\Delta H$ and $\Delta S$ were found to be both $+\text{ve}$. If $T_e$ is the temperature at equilibrium, the reaction would be spontaneous when:

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from $V$ to $32V$, the efficiency of the engine is:

A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by:

One kg of a diatomic gas is at a pressure of $8\times 10^4{\text{N/m}}^2$. The density of the gas is $4{\text{kg/m}}^3$. What is the energy of the gas due to its thermal motion?

A Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by $62\text{K}$, its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are, respectively:

$100\text{g}$ of water is heated from $30^{\circ }\text{C}$ to $50^{\circ }\text{C}$. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is $4184\text{J/kg/K}$):

The entropy change involved in the isothermal reversible expansion of $2\text{moles}$ of an ideal gas from a volume of $10{\text{dm}}^3$ to a volume of $100{\text{dm}}^3$ at $27^{\circ }\text{C}$ is:

Helium gas goes through a cycle $ABCDA$ (consisting of two isochoric and two isobaric lines) as shown in figure. The pressure and volume at $A$ are $P_0,V_0$ and at $C$ are $2P_0,2V_0$. Efficiency of this cycle is nearly:

A liquid in a beaker has temperature $\theta (t)$ at time $t$ and ${\theta }_0$ is temperature of surroundings, then according to Newton's law of cooling the correct graph between $\ln (\theta -{\theta }_0)$ and $t$ is:

A Carnot engine, whose efficiency is $40\%$, takes in heat from a source maintained at a temperature of $500\text{K}$. It is desired to have an engine of efficiency $60\%$. Then, the intake temperature for the same exhaust (sink) temperature must be:

The incorrect expression among the following is:

A system goes from A to B via two processes I and II as shown in the figure. If $\Delta U_1$ and $\Delta U_2$ are the changes in internal energies in the processes I and II respectively, then:

An ideal gas expands in volume from $1\times 10^{-3}{\text{m}}^3$ to $1\times 10^{-2}{\text{m}}^3$ at $300\text{K}$ against a constant pressure of $1\times 10^5{\text{Nm}}^{-2}$. The work done is:

Which of the following parameters does not characterize the thermodynamic state of matter?

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $C_p/C_v$ for the gas is:

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

In the nuclear fusion reaction ${}_1^2\text{H}{+}_1^3\text{H}{\to }_2^4\text{He}+\text{n}$, given that the repulsive potential energy between the two nuclei is $7.7\times 10^{-14}\text{J}$, the temperature at which the gases must be heated to initiate the reaction is nearly: (Boltzmann’s constant $k=1.38\times 10^{-23}\text{J/K}$)

According to Newton’s law of cooling, the rate of cooling of a body is proportional to $(\Delta \theta {)}^n$, where $\Delta \theta$ is the difference of the temperature of the body and the surroundings, and $n$ is equal to:

A carnot engine takes $3\times 10^6\text{cal}$ of heat from a reservoir at $627^{\circ }\text{C}$, and gives it to a sink at $27^{\circ }\text{C}$. The work done by the engine is:

The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by:

The enthalpies of combustion of carbon and carbon monoxide are $-393.5$ and $-283{\text{kJ mol}}^{-1}$ respectively. The enthalpy of formation of carbon monoxide per mole is:

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ and kept at temperatures $T_1$ and $T_2$ respectively. The radial rate of flow of heat in a substance between the two concentric sphere is proportional to:

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is:

A gaseous mixture consists of $16\text{ g}$ of helium and $16\text{ g}$ of oxygen. The ratio $C_P/C_V$ of the mixture is:

Which of the following is incorrect regarding the first law of thermodynamics?

Oxidizing power of chlorine in aqueous solution can be determined by the parameters:$\frac{1}{2}{\text{Cl}}_2(g)\stackrel{\frac{1}{2}{\Delta }_{\text{diss}}H}{\to }\text{Cl}(g)\stackrel{{\Delta }_{\text{eg}}H}{\to }{\text{Cl}}^{-}(g)\stackrel{{\Delta }_{\text{hyd}}H}{\to }{\text{Cl}}^{-}(aq)$ Using the data:${\Delta }_{\text{diss}}{H}_{{\text{Cl}}_2}=240\text{kJ/mol}$${\Delta }_{\text{eg}}{H}_{\text{Cl}}=-349\text{kJ/mol}$${\Delta }_{\text{hyd}}{H}_{\text{Cl}}=-381\text{kJ/mol}$ The energy involved in the conversion of $\frac{1}{2}{\text{Cl}}_2(g)$ to ${\text{Cl}}^{-}(aq)$ will be:

Standard entropy of ${\text{X}}_2$, ${\text{Y}}_2$ and ${\text{XY}}_3$ are $60$, $40$ and $50{\text{J K}}^{-1}{\text{mol}}^{-1}$, respectively. For the reaction $\frac{1}{2}{\text{X}}_2+\frac{3}{2}{\text{Y}}_2\to {\text{XY}}_3$, $\Delta H=-30\text{kJ}$. For the reaction to be at equilibrium, the temperature will be:

Two chambers $(V_1,P_1,T_1)$ and $(V_2,P_2,T_2)$ are separated by an insulating partition. If the partition is removed, the final equilibrium temperature is: