Relation between P, V, T, Gamma in Adiabatic Proceses

Q. A reversible cyclic process for an ideal gas is shown below. Here, P, V, and T are pressure, volume and temperature, respectively. The thermodynamic parameters q, w, H and U are heat, work enthalpy and internal energy, respectively.
The correct option(s) is/are:

1. $q_{AC}=△U_{BC}and{w}_{AB}=P_2(V_2-V_1)$
   
2. $w_{BC}=P_2(V_2-V_1)and{q}_{BC}=△H_{AC}$
3. $△H_{AC}<△U_{BC}and{q}_{AC}=△U_{BC}$
4. $q_{BC}=△H_{AC}and△H_{AC}>△U_{CA}$

Q. The work done in adiabatic compression of 2 mole of an ideal monoatomic gas by constant external pressure of 2 atm starting from initial pressure of 1 atm and initial temperature of 300K is:
(Take $R=2cal/K.mol$)

1. 720 cal
2. 800 cal
3. 550 cal
4. 360 cal

Q. If one mole of a monatomic gas $(\gamma =\frac{5}{3})$ is mixed with one mole of a diatomic gas $(\gamma =\frac{7}{5})$ the value of $\gamma$ for the mixture is:

Q. The correct figure representing isothermal and adiabatic expansion of an ideal gas from a particular initial state is:

1. B
2. C
3. D
4. A

Q. An ideal gas in a thermally insulated vessel at internal pressure$=P_1$, volume$=V_1$ and absolute temperature $=T_1$ expands irreversibly against zero external pressure as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are $P_2,V_2$ and $T_2$, respectively. For this expansion which of the following relation(s) holds true?

1. $q=0$
2. $T_2=T_1$
3. $P_2{V}_2=P_1{V}_1$
4. $P_2{V}_2^{\gamma }$

Q. Two moles of an ideal gas $(C_v=\frac{5}{2}R)$ was compressed adiabatically against constant pressure of 2 atm. Which was initially at 350 K and 1 atm pressure. The work involve in the process is equal to:
Given: ln 350 = 5.857 and $e^{6.05}=426.65$

1. 250 R
2. 300 R
3. 380 R
4. 500 R

Q. 1 mole of $N{H}_3$ gas at ${27}^{o}C$ is expanded in reversible adiabatic condition to make volume 8 times $(\gamma =1.33).$ Final temperature and magnitude of work done respectively are

1. 150 K, 900 cal
2. 150 K, 400 cal
3. 250 K, 1000 cal
4. 200 K, 800 cal

Q. Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u=\frac{U}{V}\propto T^4$ and pressure $P=\frac{1}{3}\left(\frac{U}{V}\right)$. If the shell now undergoes an adiabatic expansion the relation between T and R is:

1. $T\propto \frac{1}{R}$
2. $T\propto \frac{1}{R^3}$
3. $T\propto e^{-R}$
4. $T\propto e^{-3R}$

Q. Which of the following is incorrect, for the reversible adiabatic expansion of an ideal gas?

1. $T{V}^{\gamma -1}$ = constant
2. $P^{\gamma }{V}^{\gamma -1}$ = constant
3. $P{V}^{\gamma }$ = constant
4. $T^{\gamma }{P}^{1-\gamma }$ = constant

Q. For a reversible adiabatic ideal gas expansion, the value of $\frac{dP}{P}$ is equal to:

1. $\gamma \frac{dV}{V}$
2. $-\gamma \frac{dV}{V}$
3. $\left(\frac{\gamma }{\gamma -1}\right)\frac{dV}{V}$
4. $\frac{dV}{V}$

Q. p-V plots for two gases during adiabatic processes are shown in the following figure. Plots 1 and 2 should correspond respectively to

1. $O_{2}and{N}_2$
2. $Heand{O}_2$
3. $O_{2}andHe$
4. $HeandAr$

Q. A polyatomic gas $(\gamma =\frac{4}{3})$ is compressed to $\frac{1}{8}$ of its volume adiabatically and reversibly. If its initial pressure is $P_0$ its new pressure will be

1. $8P_0$
2. $16P_0$
3. $6P_0$
4. $2P_0$

Q. A gas $(C_{v,m}=\frac{5}{2}R)$ behaving ideally was allowed to expand reversibly and adiabatically from $1litre$ to $32litre$. It's initial temperature was ${327}^{o}C.$ The molar enthalpy change (in $Jmol{e}^{-1}$) for the process is

1. $-1125R$
2. $-575R$
3. $-1575R$
4. None of these

Q. A gas expand adiabatically at constant pressure such that
$T\propto V^{\frac{-1}{2}}$. The value of $\gamma (\frac{C_p,m}{C_v,m}$) of the gas will be:

1. 1.3
2. 1.5
3. 1.7
4. 2

Q. $2m^3$ volume of a gas ($\gamma =1.4$) at a pressure of $4\times {10}^{5}N/m^2$ is compressed adiabatically so that its volume becomes $0.5m^3$. Calculate the work done in process? (Given $4^{1.4}=6.9$)

1. $1.48\times {10}^{6}J$
2. $4.5\times {10}^{6}J$
3. $3.28\times {10}^{8}J$
4. $4.28\times {10}^{7}J$

Q. When 1 mole of a mono atomic ideal gas a T K undergoes an adiabatic change under a constant external pressure of 1 atm, its volume changes from 1L to 2L. The final temperature in Kelvin is:

1. $T$
2. $\frac{T}{2^{2/3}}$
3. $T+\frac{2}{3\times 0.0821}$
4. $T-\frac{2}{3\times 0.0821}$

Q. $10L$ of a monoatomic ideal gas at $0^{o}C$ and $5atm$ is suddenly released to $1atm$ pressure and the gas is expanded adiabatically against the constant pressure. Find the final volume $\left(inL\right)$ of the gas.

1. $10L$
2. $34L$
3. $74L$
4. $54L$

Q. One gram mol of a diatomic gas $(\gamma =1.4)$ is compressed adiabatically and reversibly so that its temperature rises from ${27}^{o}C$ to ${127}^{o}C.$ The work done (in joules )will be

Q. The First Law of Thermodynamics states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy. This means that heat energy cannot be created or destroyed. It can, however, be transferred from one location to another and converted to and from other forms of energy.

The equation for the first law of thermodynamics is given as;

$\Delta U=q+W$

Where,

• $\Delta U$ = change in internal energy of the system.
• $q$ = algebraic sum of heat transfer between system and surroundings.
• $W$ = work interaction of the system with its surroundings.

Two moles of an ideal gas expanded isothermally and reversibly from $1\text{L}\text{to}10\text{L}$ at $300\text{K}$. What is the enthalpy change?

1. $4.98\text{kJ}$
2. $11.47\text{kJ}$
3. $11.47\text{kJ}$
4. $0\text{kJ}$

Q. The rate of diffusion of $2$ gases ${}^{\prime }{A}^{\prime }$ and ${}^{\prime }{B}^{\prime }$ are in the ratio $16:3$. If the ratio of their masses present in the mixture is $2:3$. Then:

1. The ratio of their molar masses is $16:1$
2. The ratio of their molar masses is $1:4$
3. The ratio of their moles present inside the container is $1:24$
4. The ratio of their moles present inside the container is $8:3$

Q. The incorrect figure(s) representing isothermal and adiabatic expansion of an ideal gas from a particular initial state is(are):

1. A
2. B
3. C
4. D

Q. For a reversible adiabatic ideal gas expansion, the value of $\frac{dP}{P}$ is equal to:

1. $\gamma \frac{dV}{V}$
2. $-\gamma \frac{dV}{V}$
3. $\left(\frac{\gamma }{\gamma -1}\right)\frac{dV}{V}$
4. $\frac{dV}{V}$

Q. An ideal gas in thermally insulated vessel at internal pressure $=P_1$. volume $=V_1$ and absolute temperature $=T_1$ expands irrversibly against zero external pressure. as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are $P_2,V_2$ and $T_2$ respectively. for this expansion.

1. $q=0$
2. $T_2=T_1$
3. $P_2{V}_2=P_1{V}_1$
4. $P_2{V}_2^{\gamma }=P_1{V}_1^{\gamma }$

Q. When one mole of monoatomic ideal gas at T K undergoes adiabatic change under a constant external pressure of $1$ atm changes volume from $1$ litre to $2$ litres. The final temperature in Kelvin would be?

1. $\frac{T}{2^{2/3}}$
2. $T$
3. $T+\frac{2}{3\times 0.0821}$
4. $T-\frac{2}{3\times 0.0821}$

Q. Which of the following is incorrect, for the reversible adiabatic expansion of an ideal gas?

1. $P{V}^{\gamma }$ = constant
2. $T{V}^{\gamma -1}$ = constant
3. $T^{\gamma }{P}^{1-\gamma }$ = constant
4. $P^{\gamma }{V}^{\gamma -1}$ = constant

Q. p-V plots for two gases during adibatic processes are shown in the following figure. Plots 1 and 2 should correspond respectively to:

1. $He$ and $O_2$
2. $He$ and $Ar$
3. $O_2$ and $N_2$
4. $O_2$ and $He$

Q. The pressure and density of a diatomic gas $(\gamma =7/5)$ change adiabatically from (P, d) to (P, d) if $\frac{d^{\prime }}{d}=32$ then $\frac{P^{\prime }}{P}$ should be

1. None of the above
2. 128
3. 32
4. $\frac{1}{128}$

Q. p-V plots for two gases during adibatic processes are shown in the following figure. Plots 1 and 2 should correspond respectively to:

1. $He$ and $O_2$
2. $O_2$ and $He$
3. $O_2$ and $N_2$
4. $He$ and $Ar$

Q. The pressure $v/s$ volume graph of an ideal gas is given in different thermodynamics process which of the following option in relevant order: (Isochoric, isobaric, isothermal, adiabatic)

1. d, a, b, c
2. a, d, c, b
3. a, c, d, b
4. a, b, c, d

Q. Which are true for reversible adiabatic process :

1. $w=2.303RT\log \frac{V_2}{V_1}$
2. $w=\frac{nR}{(\gamma -1)}(T_2-T_1)$
3. $w=2.303RT\log \frac{V_1}{V_2}$
4. $\Delta U=w$ = $n{C}_v\Delta T$