Thermodynamics Quiz-1

The true statement amongst the following is :

Five moles of an ideal gas at 1 bar and \(298 \mathrm{~K}\) is expanded into vacuum to double the volume. The work done is :

Among the following, the set of parameters that represents path functions, is:

(A) \(q+w\)
(B) \(q\)
(C) \(w\)
(D) \(H-T S\)

Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non-expansion work is zero)

5 moles of an ideal gas at \(100 \mathrm{~K}\) are allowed to undergo reversible compression till its temperature becomes \(200 \mathrm{~K}\). If \(\mathrm{C}_V=28 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\), calculate \(\Delta \mathrm{U}\) and \(\Delta \mathrm{pV}\) for this process. \(\left(\mathrm{R}=8.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)\)

For a diatomic ideal gas in a closed system, which of the following plots does not correctly describe the relation between various thermodynamic quantities? 

The process with negative entropy change is:

Which of the following lines correctly show the temperature dependence of equilibrium constant, \(\mathrm{K}\), for an exothermic reaction?

For which of the following processes, \(\Delta \mathrm{S}\) is negative?

\(\Delta \mathrm{U}\) is equal to

A gas undergoes change from state A to state B. In this process, the heat absorbed and work done by the gas is \(5 \mathrm{~J}\) and \(8 \mathrm{~J}\), respectively. Now gas is brought back to A by another process during which \(3 \mathrm{~J}\) of heat is evolved. In this reverse process of B to A :

If 100 mole of \(\mathrm{H}_2 \mathrm{O}_2\) decomposes at 1 bar and \(300 \mathrm{~K}\), the work done \((\mathrm{kJ})\) by one mole of \(\mathrm{O}_2(\mathrm{~g})\) as it expands against 1 bar pressure is : \(\left(\mathrm{R}=83 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)\)
\(
2 \mathrm{H}_2 \mathrm{O}_2(l) \rightleftharpoons \mathrm{H}_2 \mathrm{O}(l)+\mathrm{O}_2(g)
\)

A reaction at 1 bar is non-spontaneous at low temperature but becomes spontaneous at high temperature. Identify the correct statement about the reaction among the following :

One mole of an ideal gas at \(300 \mathrm{~K}\) in thermal contact with surroundings expands isothermally from \(1.0 \mathrm{~L}\) to \(2.0 \mathrm{~L}\) against a constant pressure of \(3.0 \mathrm{~atm}\). In this process, the change in entropy of surroundings \(\left(\Delta S_{\text {surr }}\right)\) in \(\mathrm{JK}^{-1}\) is \((1 \mathrm{~L} \mathrm{~atm}=101.3 \mathrm{~J})\)

A piston filled with \(0.04 \mathrm{~mol}\) of an ideal gas expands reversibly from \(50.0 \mathrm{~mL}\) to \(375 \mathrm{~mL}\) at a constant temperature of \(37.0^{\circ} \mathrm{C}\). As it does so, it absorbs \(208 \mathrm{~J}\) of heat. The values of \(\mathrm{q}\) and \(\mathrm{w}\) for the process will be: \((\mathrm{R}=8.314 \mathrm{~J} / \mathrm{mol} \mathrm{K})(\ln 7.5=2.01)\)

Which of the following statements/relationships is not correct in thermodynamic changes?

When one mole of monoatomic ideal gas at \(T \mathrm{~K}\) undergoes adiabatic change under a constant external pressure of \(1 \mathrm{~atm}\), volume changes from 1 litre to 2 litre. The final temperature in Kelvin would be

A mono-atomic ideal gas undergoes a process in which the ratio of \(P\) to \(V\) at any instant is constant and equals to 1 . What is the molar heat

Two moles of an ideal gas is expanded isothermally and reversibly from 1 litre to 10 litres at \(300 \mathrm{~K}\). The enthalpy change (in \(\mathrm{kJ}\) ) for the process is

One mole of a non-ideal gas undergoes a change of state \((2.0 \mathrm{~atm}\), \(3.0 \mathrm{~L}, 95 \mathrm{~K}) \rightarrow(4.0 \mathrm{~atm}, 5.0 \mathrm{~L}, 245 \mathrm{~K})\) with a change in internal energy, \(\Delta U=30.0 \mathrm{~L} \mathrm{~atm}\). The change in enthalpy \((\Delta H)\) of the process in \(\mathrm{L}\) atm is

In thermodynamics, a process is called reversible when

Which one of the following statements is false?

One mole of an ideal gas is taken from \(a\) to \(b\) along two paths denoted by the solid and the dashed lines as shown in the graphs below. If the work done along the solid line path \(w_s\) and that along the dotted line path is \(w_d\), then the integer closest to the ratio \(w_d / w_s\) is:

In a constant volume calorimeter, \(3.5 \mathrm{~g}\) of a gas with molecular weight 28 was burnt in excess oxygen at \(298.0 \mathrm{~K}\). The temperature of the calorimeter was found to increase from \(298.0 \mathrm{~K}\) to \(298.45 \mathrm{~K}\) due to the combustion process. Given that the heat capacity of the calorimeter is \(2.5 \mathrm{~kJ} \mathrm{~K}^{-1}\), the numerical value for the enthalpy of combustion of the gas in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is

For a dimerization reaction, \(\quad 2 \mathrm{~A}(\mathrm{~g}) \rightarrow \mathrm{A}_2(\mathrm{~g})\), at \(298 \mathrm{~K}, \Delta \mathrm{U}^{\Theta}=-20 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta \mathrm{S}^{\Theta}=-30 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\), then the \(\Delta \mathrm{G}^{\Theta}\) will be _____ J.

One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The magnitude of the work done (by the system or on the system) is ____ \(\mathrm{J}\) (nearest integer).

\(
\text { Given }: \log 2=0.3, \ln 10=2.3
\)

An athlete is given \(100 \mathrm{~g}\) of glucose \(\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6\right)\) for energy. This is equivalent to \(1800 \mathrm{~kJ}\) of energy. The \(50 \%\) of this energy gained is utilized by the athlete for sports activities at the event. In order to avoid storage of energy, the weight of extra water he would need to perspire is ____  g (Nearest integer)
Assume that there is no other way of consuming stored energy.
Given : The enthalpy of evaporation of water is 45 \(\mathrm{kJ} \mathrm{mol}^{-1}\)
Molar mass of \(\mathrm{C}, \mathrm{H} \& \mathrm{O}\) are 12.1 and \(16 \mathrm{~g} \mathrm{~mol}^{-1}\).

The magnitude of work done by a gas that undergoes a reversible expansion along the path \(A B C\) shown in the figure is _____.

At constant volume, \(4 \mathrm{~mol}\) of an ideal gas when heated from \(300 \mathrm{~K}\) to \(500 \mathrm{~K}\) changes its internal energy by \(5000 \mathrm{~J}\). The molar heat capacity at constant volume is ________.

For the reaction, \(2 \mathrm{CO}+\mathrm{O}_2 \longrightarrow 2 \mathrm{CO}_2 ; \Delta H=-560 \mathrm{~kJ}\). Two moles of \(\mathrm{CO}\) and one mole of \(\mathrm{O}_2\) are taken in a container of volume \(1 \mathrm{~L}\). They completely form two moles of \(\mathrm{CO}_2\), the gases deviate appreciably from ideal behaviour. If the pressure in the vessel changes from 70 to \(40 \mathrm{~atm}\), find the magnitude (absolute value) of \(\Delta U\) at \(500 \mathrm{~K} .(1 \mathrm{~L} \mathrm{~atm}\) \(=0.1 \mathrm{~kJ})\)

A sample of argon gas at \(1 \mathrm{~atm}\) pressure and \(27^{\circ} \mathrm{C}\) expands reversibly and adiabatically from \(1.25 \mathrm{dm}^3\) to \(2.50 \mathrm{dm}^3\). Calculate the enthalpy change in this process. \(C_{V, m}\) for argon is \(12.48 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\).

An athlete is given \(100 \mathrm{~g}\) of glcuose \(\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6\right)\) of energy equivalent to \(1560 \mathrm{~kJ}\). He utilizes 50 percent of this gained energy in the event. In order to avoids storage of energy in the body, calculate the weight of water he would need to perspire. The enthalpy of evaporation of water is \(44 \mathrm{~kJ} / \mathrm{mole}\).

Lattice enthalpy and enthalpy of solution of \(\mathrm{NaCl}\) are \(788 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(4 \mathrm{~kJ} \mathrm{~mol}^{-1}\), respectively. The hydration enthalpy of \(\mathrm{NaCl}\) is :

For one mole of an ideal gas, which of these statements must be true?
(1) \(\mathrm{U}\) and \(\mathrm{H}\) each depends only on temperature
(2) Compressibility factor \(z\) is not equal to 1
(3) \(\mathrm{C}_{\mathrm{P}, \mathrm{m}}-\mathrm{C}_{\mathrm{V}, \mathrm{m}}=\mathrm{R}\)
(4) \(\mathrm{dU}=\mathrm{C}_{\mathrm{V}} \mathrm{dT}\) for any process

The intermolecular potential energy for the molecules \(A, B, C\) and \(D\) given below suggests that :

If enthalpy of atomisation for \(\mathrm{Br}_2(l)\) is \(x \mathrm{~kJ} / \mathrm{mol}\) and bond enthalpy for \(\mathrm{Br}_2\) is \(y \mathrm{~kJ} / \mathrm{mol}\), the relation between them:

The difference between \(\Delta \mathrm{H}\) and \(\Delta \mathrm{U}(\Delta \mathrm{H}-\Delta \mathrm{U})\), when the combustion of one mole of heptane (I) is carried out at a temperature T, is equal to

The combustion of benzene (l) gives \(\mathrm{CO}_2(\mathrm{~g})\) and \(\mathrm{H}_2 \mathrm{O}(l)\). Given that heat of combustion of benzene at constant volume is \(-3263.9 \mathrm{~kJ} \mathrm{~mol}^{-1}\) at \(25^{\circ} \mathrm{C}\); heat of combustion (in \(\mathrm{kJ} \mathrm{mol}^{-1}\) ) of benzene at constant pressure will be : \(\left(\mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)\)

For which of the following reactions, \(\Delta \mathrm{H}\) is equal to \(\Delta \mathrm{U}\) ?

Given
\(
\begin{aligned}
& \mathrm{C}_{\text {(graphite) }}+\mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}_2(\mathrm{~g}) ; \Delta_r \mathrm{H}^{\ominus}=-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{l}) ; \Delta_r \mathrm{H}^{\ominus}=-285.8 \mathrm{~kJ} \mathrm{~mol}^{-1}
\end{aligned}
\)
\(
\mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{CH}_4(\mathrm{~g})+2 \mathrm{O}_2(\mathrm{~g}); \Delta_r \mathrm{H}^{\ominus}=+890.3 \mathrm{~kJ} \mathrm{~mol}^{-1}
\)
Based on the above thermochemical equations, the value of \(\Delta_r \mathrm{H}^{\ominus}\) at \(298 \mathrm{~K}\) for the reaction
\(\mathrm{C}_{\text {(graphite) }}+2 \mathrm{H}_2(\mathrm{~g}) \rightarrow \mathrm{CH}_4(\mathrm{~g})\) will be :

For a reaction, \(\mathrm{A}(\mathrm{g}) \rightarrow \mathrm{A}(\mathrm{l}) ; \Delta \mathrm{H}=-3 \mathrm{RT}\). The correct statement for the reaction is :

The heats of combustion of carbon and carbon monoxide are -393.5 and \(-283.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\), respectively. The heat of formation (in \(\mathrm{kJ}\) ) of carbon monoxide per mole is :

The heat of atomization of methane and ethane are \(360 \mathrm{~kJ} / \mathrm{mol}\) and 620 \(\mathrm{kJ} / \mathrm{mol}\), respectively. The longest wavelength of light capable of breaking the \(\mathrm{C}-\mathrm{C}\) bond is (Avogadro number \(=6.02 \times 10^{23}, \mathrm{~h}=6.62\) \(\left.\times 10^{-34} \mathrm{~J} \mathrm{~s}\right):\)

For complete combustion of ethanol,
\(
\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(l)+3 \mathrm{O}_2(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(l)
\)
the amount of heat produced as measured in bomb calorimeter, is 1364.47 \(\mathrm{~kJ} \mathrm{~mol}{ }^{-1}\) at \(25^{\circ} \mathrm{C}\). Assuming ideality the enthalpy of combustion, \(\Delta_{\mathrm{c}} \mathrm{H}\), for the reaction will be:
\(
\left(\mathrm{R}=8.314 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)
\)

The standard enthalpy of formation of \(\mathrm{NH}_3\) is \(-46.0 \mathrm{~kJ} / \mathrm{mol}\). If the enthalpy of formation of \(\mathrm{H}_2\) from its atoms is \(-436 \mathrm{~kJ} / \mathrm{mol}\) and that of \(\mathrm{N}_2\) is \(-712 \mathrm{~kJ} / \mathrm{mol}\), the average bond enthalpy of \(\mathrm{N}-\mathrm{H}\) bond in \(\mathrm{NH}_3\) is:

For the process
\(\mathrm{H}_2 \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g})\)
at \(T=100^{\circ} \mathrm{C}\) and 1 atmosphere pressure, the correct choice is

Given
(I) \(\mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(l)\);
\(
\Delta \mathrm{H}^{\ominus}{ }_{298 \mathrm{~K}}=-285.9 \mathrm{~kJ} \mathrm{~mol}^{-1}
\)
(II) \(\mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g})\);
\(
\Delta \mathrm{H}^{\ominus}{ }_{298 \mathrm{~K}}=-241.8 \mathrm{~kJ} \mathrm{~mol}^{-1}
\)
The molar enthalpy of vapourisation of water will be :

The species which by definition has ZERO standard molar enthalpy of formation at \(298 \mathrm{~K}\) is

For the process \(\mathrm{H}_2 \mathrm{O}(1)(1 \mathrm{bar}, 373 \mathrm{~K}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g})(1 \mathrm{bar}, 373 \mathrm{~K})\), the correct set of thermodynamic parameters is

The value of \(\log _{10} K\) for a reaction \(A \rightleftharpoons B\) is (Given :
\(\Delta_r H_{298 \mathrm{~K}}^{\ominus}=-54.07 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta_r S_{298 \mathrm{~K}}^{\ominus}\)
\(=10 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\) and \(R=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\); \(2.303 \times 8.314 \times 298=5705)\)