Thermodynamic Processes

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The work of $146 kJ$ is performed in order to compress one kilo mole of a gas adiabatically and in this process, the temperature of the gas increases by $7^{\circ} C$ . The gas is ( $R = 8.3 J mol^{- 1} K^{- 1}$ )

a mixture of monatomic and diatomic

A cylinder with fixed capacity of 67.2 L contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is [Take, $R = 8.31 J mol^{- 1} K^{- 1}$ ]

Half-mole of an ideal monoatomic gas is heated at constant pressure of $1 atm$ from $2 0^{\circ} C$ to $9 0^{\circ} C$ . Work done by gas is close to (Take, gas constant, $R = 8.31 J/mol-K$ )

An ideal gas is expanding such that $p T^{3} = constant$ . The coefficient of volume expansion of the gas is

1/ T

2/ T

4/ T

3/ T

LEVELJEE Advanced

The change in the magnitude of the volume of an ideal gas when a small additional pressure $Δ p$ is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity $Δ T$ at constant pressure. The initial temperature and pressure of the gas are 300 K and 2 atm, respectively. If $∣Δ T ∣ = C ∣Δ p ∣$ , then value of $C$ (in K/atm) is ......... .

When heat $Q$ is supplied to a diatomic gas of rigid molecules, at constant volume, its temperature increases by $Δ T$ . The heat required to produce the same change in temperature, at a constant pressure is

\frac{2}{3} Q

\frac{5}{3} Q

\frac{3}{2} Q

\frac{7}{5} Q

A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is $T V^{x} = constant$ , then $x$ is

\frac{2}{5}

\frac{2}{3}

\frac{5}{3}

\frac{3}{5}

The temperature of $3.00 mol$ of an ideal diatomic gas is increased by $40. 0^{\circ} C$ without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is $x /10$ , then the value of $x$ (round off to the nearest integer) is ……… . (Given, $R = 8.31 J mol^{- 1} K^{- 1}$ )

In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $V T = k$ , where $k$ is a constant. In this process, the temperature of the gas is increased by $Δ T$ . The amount of heat absorbed by gas is (where, $R$ is gas constant)

\frac{1}{2} k R Δ T

\frac{2 k}{3} Δ T

\frac{1}{2} R Δ T

\frac{3}{2} R Δ T

The given diagram shows four processes, i.e. isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by

LEVELJEE Advanced

The net work on the gas in the cycle ABCDA is (see above figure)

A litre of dry air at STP expands adiabatically to a volume of 3 L. If $γ = 1.40$ , the work done by air is ( $3^{1.4} = 4.6555$ ) [Take, air to be an ideal gas]

LEVELJEE Advanced

One mole of an ideal gas at $2 7^{\circ} C$ is taken from $A$ to $B$ as shown in the given $p - V$ indicator diagram. The work done by the system will be ...... $\times 1 0^{- 1} J$ . [Take, $R = 8.3 J/mol-K$ , $ln 2 = 0.6931$ ] (Round off to the nearest integer)

Two moles of an ideal monoatomic gas occupies a volume $V$ at $2 7^{\circ} C$ . The gas expands adiabatically to a volume $2 V$ . Calculate (i) the final temperature of the gas and (ii) change in its internal energy.

189 K

2.7 kJ

195 K

- 2.7 kJ

189 K

- 2.7 kJ

195 K

2.7 kJ

For the given cyclic process $C A B$ as shown for a gas, the work done is

$n$ mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes. $A \to B$ : Isothermal expansion at temperature $T$ , so that the volume is doubled from $V_{1}$ to $V_{2} = 2 V_{1}$ and pressure changes from $p_{1}$ to $p_{2}$ . $B \to C$ : Isobaric compression at pressure $p_{2}$ to initial volume $V_{1}$ . $C \to A$ : Isochoric change leading to change of pressure from $p_{2}$ to $p_{1}$ . Total work done in the complete cycle ABCA is

0

n R T ln 2

n R T (ln 2 + \frac{1}{2})

n R T (ln 2 - \frac{1}{2})

The given $p - V$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

p_{0} V_{0}

(\frac{13}{2}) p_{0} V_{0}

(\frac{11}{2}) p_{0} V_{0}

4 p_{0} V_{0}

A balloon filled with helium ( $3 2^{\circ} C$ and $1.7 atm$ ) bursts. Immediately afterwards; the expansion of helium can be considered as

irreversible isothermal

irreversible adiabatic

reversible adiabatic

reversible isothermal

Which of the following parameters does not characterise the thermodynamic state of matter?

LEVELJEE Advanced

If one mole of an ideal gas at $(p_{1}, V_{1})$ is allowed to expand reversibly and isothermally ( $A$ to $B$ ), its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value ( $B \to C$ ). Then, it is restored to its initial state by a reversible adiabatic compression ( $C$ to $A$ ). The net work done by the gas is equal to

R T (ln 2 - \frac{1}{2 ( γ - 1 )})

- \frac{R T}{2 ( γ - 1 )}

0

R T ln 2

A monoatomic ideal gas, initially at temperature $T_{1}$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_{2}$ by releasing the piston suddenly. If $l_{1}$ and $l_{2}$ are the lengths of the gas column, before and after the expansion respectively, then the value of $\frac{T _{1}}{T _{2}}$ will be

(\frac{l _{1}}{l _{2}})^{\frac{2}{3}}

(\frac{l _{2}}{l _{1}})^{\frac{2}{3}}

\frac{l _{2}}{l _{1}}

\frac{l _{1}}{l _{2}}

In the reported figure, there is a cyclic process ABCDA on a sample of $1 mol$ of a diatomic gas. The temperature of the gas during the process $A \to B$ and $C \to D$ are $T_{1}$ and $T_{2}$ ( $T_{1} > T_{2}$ ), respectively. Choose the correct option out of the following for work done, if processes BC and DA are adiabatic.

W_{A B} = W_{D C}

W_{A D} = W_{B C}

W_{B C} + W_{D A} > 0

W_{A B} < W_{C D}

LEVELJEE Advanced

$n$ moles of an ideal gas undergoes a process $A$ and $B$ as shown in the figure. The maximum temperature of the gas during the process will be

\frac{9}{4} \frac{p _{0} V _{0}}{n R}

\frac{3}{2} \frac{p _{0} V _{0}}{n R}

\frac{9}{2} \frac{p _{0} V _{0}}{n R}

\frac{9 p _{0} V _{0}}{n R}

Match List-I with List-II. \begin{array}{ll} \text{List-I} & \text{List-II} \\ \text{A. Isothermal} & \text{1. Pressure constant} \\ \text{B. Isochoric} & \text{2. Temperature constant} \\ \text{C. Adiabatic} & \text{3. Volume constant} \\ \text{D. Isobaric} & \text{4. Heat content is constant} \end{array} Choose the correct answer from the options given below.

\to

\to

\to

\to

\to

\to

\to

\to

\to

\to

\to

\to

\to

\to

\to

\to

LEVELJEE Advanced

Starting at temperature $300 K$ , one mole of an ideal diatomic gas ( $γ = 1.4$ ) is first compressed adiabatically from volume $V_{1}$ to $V_{2} = \frac{V _{1}}{16}$ . It is then allowed to expand isobarically to volume $2 V_{2}$ . If all the processes are the quasi-static, then the final temperature of the gas (in $^{\circ} K$ ) is (to the nearest integer) ......... .