Thermodynamic Processes

Q. The relation between internal energy $U$, pressure $P$ and volume $V$ of a gas in an adiabatic process is $U=a+bPV$, where $a$ and $b$ are constants. What is the effective value of adiabatic constant $\gamma$?

1. $\frac{a}{b}$
2. $\frac{b+1}{b}$
3. $\frac{a+1}{a}$
4. $\frac{b}{a}$

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. $68.7\text{atm}$
4. $28\text{atm}$

Q.

An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to __________.

Q. $P-V$ plots for two gases during adiabatic processes are shown in Fig. Plots 1 and 2 should correspond respectively to

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

Q. The slopes of isothermal and adiabatic curves are related as

(a) Isothermal curve slope = adiabatic curve slope
(b) Isothermal curve slope = $\gamma X$ adiabatic curve slope
(c) Adiabatic curve slope = $\gamma X$ isothermal curve slope
(d) Adiabatic curve slope = $\frac{1}{2}X$ isothermal curve slope

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

Q. Three moles of an ideal gas are taken through a cyclic process $ABCA$ as shown in $T-V$ indicator diagram. The gas loses $2510\text{J}$ of heat in the complete cycle. If $T_A=100\text{K}$ and $T_B=200\text{K}$, the work done by the gas during the process $BC$ is (line AB if extended passes through origin)

1. $5000\text{J}$
2. $-5000\text{J}$
3. $4000\text{J}$
4. $-2500\text{J}$

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. The molar heat capacity in a process of a diatomic gas, if it does a work of $\frac{Q}{4},$ when a heat of $Q$ is supplied to it is

1. $\frac{2}{5}R$
2. $\frac{10}{3}R$
3. $\frac{5}{2}R$
4. $\frac{6}{7}R$

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. $24\text{kJ}$
4. $120\text{kJ}$

Q. An ideal gas has initial volume $V$ and pressure $p$. If the volume of gas is doubled during expansion, then minimum work will be done in which thermodynamic process ?

1. Isobaric process
2. Isothermal process
3. Adiabatic process
4. Same in all alone given process

Q. During an experiment an ideal gas is found to obey the condition $\frac{P^2}{\rho }=\text{constant}$ [$\rho$ is the density of the gas]. The gas is initially at temperature $T$, pressure $P$ and density $\rho$. If the gas expands such that density changes to $\frac{\rho }{2}$ , then choose the correct answer(s).

1. Pressure of the gas changes to $\sqrt{2}P$
2. The temperature of the gas changes to $\sqrt{2}T$
3. The $P-T$ Indicator diagram of the above process is a parabola.
4. The $P-T$ Indicator diagram of the above process is a Rectangular hyperbola.

Q.

A typical dorm room or bedroom contains about 2500 moles of air. Find the change in the internal energy of this much air when it is cooled from ${35.0}^{\circ }C$ to ${26.0}^{\circ }C$ at a constant pressure of 1.00 atm. Treat the air as an ideal gas with $\gamma =1.400$.

1. 

2. 

3. 

4. 

Q. A mixture of hydrogen and oxygen has volume $500{\text{cm}}^3,$ temperature $300\text{K},$ pressure $400\text{kPa}$ and mass $0.76\text{g}.$ The ratio of masses of oxygen to hydrogen will be

1. $16:3$
2. $3:16$
3. $8:3$
4. $3:8$

Q. Heat is supplied to a diatomic gas at a constant pressure. The ratio of $\Delta Q:\Delta U:\Delta W$ is

1. $5:3:2$
2. $5:2:3$
3. $7:5:2$
4. $7:2:5$

Q. In an adiabatic process, pressure is increased by $\frac{2}{3}\%$. If $\frac{C_P}{C_V}=\frac{3}{2}$, then the volume decreases by about

1. $\frac{4}{9}\%$
2. $\frac{2}{3}\%$
3. $4\%$
4. $\frac{9}{4}\%$

Q. If a gas is taken from $A$ to $C$ through $B$, then heat absorbed by the gas is $8\text{J}$. Heat absorbed by the gas in taking it directly from $A$ to $C$ is

1. $+8\text{J}$
2. $+9\text{J}$
3. $+5\text{J}$
4. $+7\text{J}$

Q. If heat is given to an ideal gas at constant pressure, then select the graph which best represents the variation of $VT$ with temperature $\left(T\right)$.

1. 
2. 
3. 
4. 

Q. An ideal monatomic gas at $300\text{K}$ expands adiabatically to $8$ times its volume. What is the final temperature?

1. $300\text{K}$
2. $75\text{K}$
3. $560\text{K}$
4. $340\text{K}$

Q.

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature $\mathrm{T}$ ? (${\mathrm{k}}_{\mathrm{B}}$ is Boltzmann constant)

1. ${\mathrm{K}}_{\mathrm{B}}\mathrm{T}$

2. $\frac{2}{3}{\mathrm{K}}_{\mathrm{B}}\mathrm{T}$

3. $\frac{3}{2}{\mathrm{K}}_{\mathrm{B}}\mathrm{T}$

4. $\frac{1}{2}{\mathrm{K}}_{\mathrm{B}}\mathrm{T}$

Q.

Why is the work done in a reversible process maximum?

Q. Pressure versus temperature graphs of an ideal gas are as shown in figure. Choose the wrong statement

1. Density of gas is constant in graph (iii)
2. Density of gas is increasing in graph (i)
3. Density of gas is decreasing in graph (ii)
4. None of these

Q.

Why Gibbs free energy is called free energy?

Q. $P-V$ diagram of a diatomic gas is a straight line passing through origin. What is the molar heat capacity of the gas during the process?

1. $R$
2. $2R$
3. $3.33R$
4. $3R$

Q. In which process, the $PV$ indicator diagram is a straight line parallel to volume axis?

1. Isothermal
2. Isobaric
3. Irreversible
4. Adiabatic

Q. An ideal gas at ${27}^{\circ }$C is compressed adiabatically to $\frac{8}{27}$ of its originalvolume. If $\gamma =\frac{5}{3}$, then the rise in temperature is

1. 225 K
2. 405 K
3. 375 K
4. 450 K

Q. Bursting of a tyre is an example of which of the following processes?

1. Isobaric
2. Adiabatic
3. Isochoric
4. Isothermal

Q. An ideal gas undergoes a cyclic process $\text{abcda}$ which is shown by the pressure - density curve.

1. Work done by the gas in the process $bc$ is zero.
2. Work done by the gas in the process $cd$ is negative.
3. Internal energy of the gas in state $a$ is greater than in state $c$.
4. Net work done by the gas in the cycle is negative.

Q. $105$ calories of heat is required to raise the temperature of $3$ moles of an ideal gas at constant pressure from ${30}^{\circ }\text{C}$ to ${35}^{\circ }\text{C}$. The amount of heat required in calories to raise the temperature of the gas from ${60}^{\circ }\text{C}$ to ${65}^{\circ }\text{C}$ at constant volume is $[\gamma =\frac{C_P}{C_V}=1.4]$

1. $50\text{cal}$
2. $75\text{cal}$
3. $70\text{cal}$
4. $90\text{cal}$

Q. 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 $\left(\frac{7}{3}\right)T_0$. The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (Ignore the heat capacity of boxes). Then, the final temperature of the gases, $T_f$ in terms of $T_0$ is -

1. $T_f=\frac{3}{7}{T}_0$
2. $T_f=\frac{7}{3}{T}_0$
3. $T_f=\frac{3}{2}{T}_0$
4. $T_f=\frac{5}{2}{T}_0$

Q. One mole of an ideal monoatomic gas is taken from A to C along the path ABC. The temperature of the gas at A is $T_0$. For the process ABC, which one of the following option(s) is/are correct?

1. Work done by the gas is $R{T}_0$.
2. Change in internal energy of the gas is $\frac{11}{2}R{T}_0$.
3. Heat absorbed by the gas is $\frac{11}{2}R{T}_0$.
4. Heat absorbed by the gas is $\frac{13}{2}R{T}_0$.