Thermodynamic Processes

Q.

Calculate the value of mean free path $\left(\lambda \right)$ for oxygen molecules at temperature $27°C$ and pressure $1.01\times {10}^{5}Pa$. Assume the molecular diameter $0.3nm$ and the gas is ideal. $\left(1.38\times {10}^{-23}j{K}^{-1}\right)$.

1. $102nm$

2. $32nm$

3. $58nm$

4. $86nm$

Q. Work done in the cyclic process shown in the figure is -

1. $4P_0{V}_0$
2. $-4P_0{V}_0$
3. $-\pi P_0{V}_0$
4. $\pi P_0{V}_0$

Q.

For one mole of an ideal gas, which of these statements must be true?

1) (a), (c) and (d)

2) (a) and (c)

3) (c) and (d)

4) (b), (c) and (d)

1. $\mathrm{U}$ and $\mathrm{H}$ each depend only on the temperature

2. Compressibility factor $\mathrm{z}$ 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

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. A cylinder having a piston contains $1\text{mole}$ of methane gas at $100\text{kPa}$ and ${20}^{\circ }C$. The gas is compressed reversibly to a pressure of $800\text{kPa}$. If the process is polytropic with exponent $x=1.15$, then the work required (in $\text{kJ}$) is (nearest integer value)
[Take $R$ for methane $=8.314\text{J/mol K}$ and $8^{0.13}=1.31$]

Q. A gas undergoes a cyclic process as shown in the $P-V$ diagram. For one complete cycle, choose the correct option among the following.

1. Change in internal energy = 0, heat supplied < 0
2. Change in internal energy = 0, heat supplied > 0
3. Change in internal energy > 0, heat supplied < 0
4. Change in internal energy < 0, heat supplied > 0

Q. For adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to :

1. $-\gamma \frac{V}{dV}$
2. $-\frac{dV}{\gamma V}$
3. $\frac{dV}{V}$
4. $-\gamma \frac{dV}{V}$

Q. Calculate the magnitude of work done when 4 moles of a perfect gas are compressed adiabatically. The initial pressure and volume of the gas are ${10}^5{\text{N/m}}^2$ and 8 litres respectively. The final volume of the gas is 4 litres. Molar specific heat of the gas at constant volume is $3R/2$.

1. $800\text{J}$
2. $705\text{J}$
3. $815\text{J}$
4. $725\text{J}$

Q. An ideal gas expands while the pressure is kept constant. During this process

1. $Q$ is positive
2. $Q$ is negative
3. $Q$ is equal to zero
4. Depends upon number of moles.

Q. The given figure shows an isochoric process, an isothermal process, an adiabatic process and two isobaric processes (one for monoatomic gas and other for diatomic) on a work done $\left(W\right)$ versus heat supplied$\left(Q\right)$ curve. The initial states of both gases are the same and the scales for the two axes are same.



Which of the following statements is incorrect?

1. Straight line $1$ corresponds to an isochoric process.
2. Straight line $2$ corresponds to an isobaric process for diatomic gas.
3. Straight line $4$ corresponds to an isothermal process.
4. Straight line $1$ corresponds to an isothermal process.

Q. Figure shows a cylindrical container containing oxygen gas and closed by a piston of mass $50\text{kg}$. Piston can slide smoothly in the cylinder. Its cross sectional area is $100{\text{cm}}^2$ and atmospheric pressure is ${10}^5\text{Pa}$. Some heat is supplied to the cylinder so that the piston is slowly displaced up by $20\text{cm}$.
Find the amount of heat supplied to the gas.

1. $1050\text{J}$
2. $750\text{J}$
3. $105\text{J}$
4. $1505\text{J}$

Q. A monoatomic gas undergoes an adiabatic process as indicated in the given figure. Find the work done during the process.

1. ${10}^5\text{J}$
2. $2\times {10}^5\text{J}$
3. $3\times {10}^5\text{J}$
4. $4\times {10}^5\text{J}$

Q.

Find the final temperature of one mole of an ideal gas that has an initial temperature $tK$. The gas does $9R$ joules of work adiabatically. The ratio of specific heats of this gas at constant pressure and at constant volume is $\frac{4}{3}$.

Q. A graph of pressure versus volume for an ideal gas for isochoric, isobaric, isothermal and adiabatic processes is given. Which one is for the adiabatic process?

1. $OA$
2. $OB$
3. $OC$
4. $OD$

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

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

Q. On a $P-T$ diagram, a cyclic process is performed as shown. Where is the volume maximum?

1. $\text{a}$
2. $\text{b}$
3. $\text{c}$
4. $\text{d}$

Q. The $P-V$ plots for two gases each undergoing an adiabatic process are as shown in the figure. The graphs 1 and 2 can correspond to :-

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

Q. To an ideal non-linear triatomic gas, $800\text{cal}$ of heat energy is given at constant pressure. If vibrational modes are neglected, then the energy used by the gas in doing work against the surroundings is

1. $200\text{cal}$
2. $300\text{cal}$
3. $400\text{cal}$
4. $60\text{cal}$

Q. One $\text{mole}$ of a gas in a cylinder is compressed from $8{\text{m}}^3$ to $2{\text{m}}^3$ quasi-statically at a constant temperature of $300\text{K}$. Workdone during this process is
($\ln 2=0.693$)

1. $3455\text{J}$
2. $-3455\text{J}$
3. $1728\text{J}$
4. $-1728\text{J}$

Q. A closed tank containing air is stirred by a paddle wheel. The work input to the wheel is $40\text{J}$ and the heat transformed to the surrounding from the tank is $10\text{J}$. The external workdone by the system is

1. $10\text{J}$
2. $40\text{J}$
3. $30\text{J}$
4. Zero

Q. A certain gas is taken to the five states represented by dots in the graph. The plotted lines are isotherms. Order of the most probable speed $v_p$ of the molecules at these five states is

1. $V_{pat3}>V_{pat1}=V_{pat2}>V_{pat4}=V_{pat5}$
2. $V_{pat1}>V_{pat2}=V_{pat3}>V_{pat4}=V_{pat5}$
3. $V_{pat3}>V_{pat2}=V_{pat4}>V_{pat1}=V_{pat5}$
4. Insufficient information to predict the result.

Q. Which of the following statements is true in respect of usual quantities represented by $\Delta Q$, $\Delta U$ and $\Delta W$ ?

1. $\Delta U$ and $\Delta W$ are path dependent.
2. $\Delta U$ and $\Delta Q$ are path dependent.
3. $\Delta U$ does not depend on path.
4. $\Delta Q$ does not depend upon path.

Q. For $V-T$ diagrams of two process $ab$ and $cd$ shown in figure for same gas, match the following two columns and find the correct option.
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{(a) Work done}& \text{(p) is more in process ab}\\ \text{(b) Change in internal energy}& \text{(q) is more in process cd}\\ \text{(c) Heat exchange}& \text{(r) is same in both process}\\ \text{(d) Molar heat capacity}& \text{(s) can't say anything}\end{array}$

1. $a\to s;b\to s;c\to s;d\to r$
2. $a\to q;b\to r;c\to p;d\to r$
3. $a\to r;b\to q;c\to s;d\to s$
4. $a\to s;b\to p;c\to q;d\to r$

Q. A sample of gas ($\gamma =1.5$) is taken through an adiabatic process in which the volume is compressed from $2000{\text{cm}}^3$ to $500{\text{cm}}^3$. If the initial pressure is $120\text{kPa}$, then:

1. The final pressure at point 2 is $960\text{kPa}$.
2. Heat transferred, $\Delta Q_{12}=0$.
3. Work done on the gas is $480\text{J}$.
4. The final pressure at point 2 is $480\text{kPa}$.

Q. A smooth piston of mass $m$ and cross - section area $A$ is in equilibrium on a diatomic gas filled in a cylindrical container and there is vaccum above the piston. The piston and container are non - conducting and the height of gas column in the container is $l_0$ at equilibrium. If the piston is displaced slightly down the equilibrium position, then the time period of its oscillation will be:

1. $2\pi \sqrt{\frac{10l_0}{7g}}$
2. $2\pi \sqrt{\frac{7l_0}{10g}}$
3. $2\pi \sqrt{\frac{7l_0}{5g}}$
4. $2\pi \sqrt{\frac{5l_0}{7g}}$

Q. In the figure, $n$ moles of a monoatomic ideal gas undergo the process $ABC$ as shown in the $P-V$ diagram. The process $AB$ is isothermal and $BC$ is isochoric. The temperature of the gas at $A$ is $T_0.$ Total heat given to the gas during the process $ABC$ is measured to be $Q$.


Heat absorbed by the gas in the process $BC$ is

1. $3nR{T}_0$
2. $nR{T}_0$
3. $2nR{T}_0$
4. $6nR{T}_0$

Q. Three processes completes a thermodynamic cycle for an ideal gas as shown in the $P-V$ diagram . Find the processes in correct sequential order.

1. $1\to 2$ Isothermal expansion
   $2\to 3$ Isochoric process
   $3\to 1$ Adiabatic expansion
2. $1\to 2$ Isothermal expansion
   $2\to 3$ Isochoric process
   $3\to 1$ Adiabatic compression
3. $1\to 2$ Adiabatic compression
   $2\to 3$ Isochoric process
   $3\to 1$ Isothermal compression
4. $1\to 2$ Isothermal expansion
   $2\to 3$ Isochoric process
   $3\to 1$ Isothermal compression

Q. The volume $\left(V\right)$ versus temperature $\left(T\right)$ graph of an ideal gas of given mass, undergoing a thermodynamic process is shown below. During this process, if the temperature increases, then the pressure of the gas

1. first increases then decreases
2. continuously decreases
3. continuously increases
4. first decreases then increases

Q. An ideal gas expands according to the law $P{V}^{3/2}=\text{constant}$. We conclude

1. The adiabatic exponent of the gas $K=1.5$
2. The molar heat capacity $C=C_v-2R$
3. Temperature increases during the process
4. Such a process is not feasible