Thermodynamic Processes

Q. 7. The volume of an air bubble is doubled as it rises o from the bottom of lake to its surface. The atmospheric pressure is 75 cm of mercury. The ratio of density of mercury to that of lake water is40/3. The depth of the lake in metre is (1) 10 (2) 15 (3) 20 (4) 2

Q. What amount of heat must be supplied to 2.0 × 10¯² kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure ? (Molecular mass of N² = 28; R = 8.3 J mol–¯¹ K¯¹.)

Q. One mole of an ideal monoatomic gas is mixed with 3 moles of an ideal diatomic gas. What is the molar specific heat(in Cal) of the mixture at constant volume ?

Q.

In thermodynamics, the 𝑃 - 𝑉 work done is given by:

w =−∫ dVP_ext

. For a system undergoing a particular process, the work done is:

w =−∫ dV (RT/V-b − a/V²)

This equation is applicable to a

a) System that satisfies the van der Waals equation of state.

b) Process that is reversible and isothermal.

c) Process that is reversible and adiabatic.

d) Process that is irreversible and at constant pressure.

Q. Which reaction, with the following values of AH, AS, at 400 K is spontaneous an d endothermic?AH=-48 kJ; AS = + 135 J/K(2) AH =-48 kJ; AS =- 135 J/K135 J/K73) AH = +48 kJ; AS- 135 J/K+48 kJ; AS( 4 ) Δ Η-

Q. 20. Calculate G° at 25° C for the reaction, 2NO2(g) N2O4(g) Given, H° = –57.20 kJ mol–1 and S° = –175.83 J mol–1 K–1. Is the reaction spontaneous or non-spontaneous?

Q. discuss the condition for a process to be sponteneous in terms of entropy and Gibbs functio

Q. 10. For endothermic reaction to be spontaneous change in entropy should be?

Q. In which process work acts as a state function :- (1) Isobaric process (2) Isochoric process (3) Adiabatic process (4) Both (1) & (2)

Q. The pressure (P) of an ideal gas of volume (V) varies as P∝V2. The slope of its P-V graph at a point i

Q. A gas is held within a closed chamber. It is undergoing a cyclic process as shown in the figure. The energy removed as heat $Q_{CA}$ during iso-choric process $CA$ is $20\text{J}$. No energy is transferred as heat during adiabatic process $BC$ and net work done during the cyclic process is $15\text{J}$. Determine the energy transferred by the system as heat during iso-baric process $AB$.

1. $10\text{J}$ of heat is absorbed by the gas.
2. $10\text{J}$ of heat is released by the gas.
3. $5\text{J}$ of heat is absorbed by the gas.
4. $5\text{J}$ of heat is released by the gas.

Q. When gas in a vessel expands its thermal energy decreases the process involved is A) isobaric B) isochoric C) isothermal D) adiabatic

Q. A fixed mass of a gas is first heated isobarically to double the volume and then cooled isochorically to decrease the temperature back to the initial value . by what factor would the process of change of state been isothermal.

Q. A diatomic gas $(\gamma =1.4)$ of mass $m$ at a pressure of $2$ atmospheres is compressed adiabatically so that its temperature rises from ${27}^{\circ }\text{C}$ to ${927}^{\circ }\text{C}.$ The pressure of the gas in final state is

1. $256\text{atm}$
2. $8\text{atm}$
3. $28\text{atm}$
4. $68.7\text{atm}$

Q. What is difference between isenthalpic and adiabatic process?

Q. 51 Two moles of a gas at 1 bar and 298 Kelvin are compressed at constant temperature by the use of a constant pressure of 5 bar how much work is done on the gas? 1)2384R

Q. In a cyclic process, a gas is taken from state $A$ to $B$ via path $-\text{I}$ as shown in the indicator diagram and taken back to state $A$ from state $B$ via path$-\text{II}$. In the complete cycle:

1. Work is done on the gas
2. Heat is given to the gas
3. Work is done by the gas
4. Heat is taken from the gas

Q. 37. Is every precipitation reaction spontaneous?

Q. Oxygen gas which is at a pressure of $2^{3/5}\text{atm}$ is compressed adiabatically so that volume becomes half that of the initial volume. The final pressure of the gas is

1. $0.25\text{atm}$
2. $0.6\text{atm}$
3. $4\text{atm}$
4. $8\text{atm}$

Q. in a thermodynamics process amount of heat given to O2 gas is equal to decrease in its internal energy correct equation of process is PV^6/5 = C PV^2 = C PV^2/3 = C P^2V^3 = Constant

Q. One mole of an ideal gas undergoes a process in which $T=T_0+a{V}^3$, where $T_0$ and '$a$' are positive constants and $V$ is the volume. The volume for which the pressure of the gas will be minimum is

1. ${\left(\frac{T_0}{2a}\right)}^{1/3}$
2. ${\left(\frac{T_0}{3a}\right)}^{1/3}$
3. ${\left(\frac{a}{2T_0}\right)}^{2/3}$
4. ${\left(\frac{a}{2T_0}\right)}^{2/3}$

Q. Consider the four processes $A,B,C,D$ shown in the graph given below

List I shows process & List II gives value of index ${}^{\prime }{n}^{\prime }$ for the equation $P{V}^n=\text{const}$
Match List I with list II.
$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ A.& A& 1.& 0\\ B& B& 2& 1\\ C& C& 3.& 1.4\\ D& D& 4.& \infty \end{array}$

1. $A-4,B-2,C-3,D-1$
2. $A-1,B-2,C-3,D-4$
3. $A-1,B-3,C-2,D-4$
4. $A-4,B-3,C-2,D-1$

Q. Figure shows a curve on $\log T$ and $\log V$ scale, when an ideal gas is undergoing an adibatic process. The gas is

1. Monatomic
2. Diatomic
3. Polyatomic
4. Mixture of monatomic and diatomic

Q. One mole of an ideal monoatomic gas has initial temperature $T_0$ is made to go through the cyclic process $abca$ as shown in figure. If $\text{U}$ denotes the internal energy, then choose the correct alternative.

1. $U_c>U_b>U_a$
2. $U_c-U_b=3R{T}_0$
3. $U_c-U_A=\frac{9R{T}_0}{2}$
4. $U_b-U_a=\frac{3R{T}_0}{2}$

Q. 11) Some heat is supplied to an ideal monoatomic gas under constant pressure. The part of the heat which goes to increase its internal energy will be a) 2/3 b) 3/5 c) 2/7 d) 5/7

Q. An ideal gas expands isothermally from volume $V_1$ to $V_2$ and is then compressed to original volume $V_1$ adiabatically. Initial pressure is $P_1$ and final pressure is $P_3$. The total work done by gas during the whole process is $W$. Then identify the correct statement.

1. $P_3>P_1,W>0$
2. $P_3<P_1,W<0$
3. $P_3>P_1,W<0$
4. $P_3=P_1,W=0$

Q. An ideal monatomic gas is confined in a horizontal cylinder by a spring - loaded piston (as shown in the figure). Initially the gas is at temperature $T_1$, pressure $p_1$ and volume $V_1$ and the spring is in its relaxed state. The gas is then heated very slowly to temperature $T_2$, pressure $p_2$ and volume $V_2$.
During this process the piston moves out by a distance $x$. Which of the following statements is /are correct?
(Ignore the friction between the piston and the cylinder).

1. If $V_2=2V_1$ and $T_2=3T_1,$ then the energy stored in the spring is $\frac{1}{4}{p}_1{V}_1$.
2. If $V_2=2V_1$ and $T_2=3T_1,$ then the change in internal energy is $3p_1{V}_1$
3. If $V_2=3V_1$ and $T_2=4T_1,$ then the work done by the gas is $\frac{7}{3}{p}_1{V}_1$.
4. If $V_2=3V_1$ and $T_2=4T_1,$ then the heat supplied to the gas is $\frac{17}{6}{p}_1{V}_1$.

Q. $3$ moles of an ideal monoatomic gas perfoms a cycle shown in the figure. The gas temperature at $A,B,C,D$ are $T_A=400K,$ $T_B=800K,T_C=2400K,T_D=1200K.$ Find the work done by the gas.

1. $12\text{kJ}$
2. $20\text{kJ}$
3. $120\text{kJ}$
4. $24\text{kJ}$

Q. Test if the following equations are dimensionally correct:
(a) $h=\frac{2S\mathrm{cos\theta }}{\rho rg},$

(b) $v=\sqrt{\frac{P}{\rho }},$

(c) $V=\frac{\pi P{r}^{4}t}{8\eta l}$

(d) $v=\frac{1}{2\pi }\sqrt{\frac{mgl}{I}};$
where h = height, S = surface tension, $\rho$ = density, P = pressure, V = volume, $\eta =$ coefficient of viscosity, v = frequency and I = moment of interia.

Q. The temperature of gas is increased from $400\text{K}$ to $600\text{K}$ keeping the volume of the gas constant. If initially the gas exerted a pressure of $3\text{kPa}$ on the walls of the container, then the final pressure of the gas is (in $\text{kPa}$)

1. $6$
2. $4.5$
3. $0.045$
4. $0.06$