One mole of an ideal gas passes through a process where pressure and volume obey the relation $P = P_0 [ 1- \frac{1}{2}\left ( \frac{V_0}{V} \right )^2]$ .Here $P_0$ and $V_0$ are constant. Calculate the change in temperature of gas if its volume changes from $V_0 \: \: to \: \: 2 V_0$ :

$\frac{1P_0 V_0 }{2R}$

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$\frac{5 P_0 V_0 }{4 R}$

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$\frac{3 P_0 V_0 }{4 R}$

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$\frac{ P_{0} V_{0}}{4 R}$

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In the given (V - T) diagram, what is the relation between pressures P₁ and P₂ ?

Cannot be predicted

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P₂ = P₁

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P₂> P₁

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P₂< P₁

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During an experiment an ideal gas is found to obey an additional law $\mathrm{ \mathrm{VP}^2= }$ constant. The gas is initially at temp $\mathrm{ T }$ and volume $\mathrm{ V }$ . What will be the temperature of the gas when it expands to a volume $\mathrm{ 2 \mathrm{~V} }$ ?

$\mathrm{T^{\prime}=\sqrt{4} T}$

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$\mathrm{{T}^{\prime}=\sqrt{2} \mathrm{~T}}$

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$\mathrm{T^{\prime}=\sqrt{5} T}$

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$\mathrm{T^{\prime}=\sqrt{6} T}$

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A monatomic ideal gas, initially at temperature $\mathrm{T_1}$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $\mathrm{T_2}$ by releasing the piston suddenly. If $\mathrm{L_1\: and \: L_2}$ are the lengths of the gas column before and after expansion respectively. then $\mathrm{\mathrm{T}_1 / \mathrm{T}_2}$ is given by

$\mathrm{{\left(L_1 / L_2\right)^{2 / 3}}}$

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$\mathrm{{{L_1} / {L_2}}}$

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${\mathrm{L}}_2 / \mathrm{L}_1$

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$\mathrm{{\left(L_2 / L_1\right)^{2 / 3}}}$

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A gas at atmospheric pressure is contained in a cylinder of volume 80 litre. When it is compressed adiabatically to 20 litre its pressure rises to $\mathrm{7 \mathrm{~atm}}$ . What will be the ratio of the specific heat of the gas?

$1.33$

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$1.4$

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$1.67$

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$1.5$

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An ideal gas is taken from the state A(p, V) to the state B(p/2,2V) along a straight line path as shown in figure. select the correct statement from the following

Work done by the gas in going from A to B exceeds the work done in going from A to B under isothermal conditions

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In the T − V diagram, path AB would become a hyperbola,

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In the p − T diagram, path AB would be part of hyperbola

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In going from A to B, the temperature T of gas first increases to a maximum value 1 and then decreases

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An ideal gas is taken from state A (pressure P, volume V) to state B (pressure P/2, volume 2V) along a straight line in the P − V diagram as shown in fig. Then which is incorrect

The work done by the gas in the process A to B exceeds the work that would be done by it if the system were taken from A to B along the isotherm

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In the T-V diagram, the path AB becomes a part of a parabola

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In the P-T diagram, the path AB becomes a part of a hyperbola

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In going from A to B, the temperature T of the gas first increases to a maximum and then decreases

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Figure shows the P − V diagram for an ideal gas. From the graph we conclude that

The process A → B is adiabatic

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The internal energy of the gas increases in this process

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The work done by the gas = area of triangle ABC

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The heat energy absorbed by the gas is zero in the process

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One mole of an ideal gas initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is $\mathrm{P}_0$. Choose the correct option (s) from the following.

Internal energies at A and B are the same

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Work done by the gas in process AB is $\mathrm{p}_0 \mathrm{~V}_0 \ln 4$

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Pressure at $C$ is $\frac{\mathrm{p}_0}{4}$

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Both a and b

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At $27^{\circ} \mathrm{C}$ two moles of an ideal monoatomic gas occupy a volume $\mathrm{\mathrm{V}}$ . The gas expands adiabatically to a volume $\mathrm{\mathrm{2V}}$ .The final temperature of the gas is:

$150 \mathrm{~K}$

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$162 \mathrm{~K}$

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$173 \mathrm{~K}$

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$189 \mathrm{~K}$

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Concepts Covered - 1

Thermodynamic variables and equation of state

Thermodynamic variables : Any thermodynamic system can be described by specifying some of the variables i.e; its pressure(P), volume(V), temperature(T), internal energy(U) and the number of moles(n). These parameters are called thermodynamic variables.

Extensive and Intensive properties/variables -

Intensive properties do not depend on the amount of matter that is present. These are bulk properties. Examples of intensive properties are - Density, Temperature ets.
Extensive properties are those properties which depend on the amount of matter that is present. Examples of extensive properties are - Volume, Weight etc.

Equation of state - The relation between the thermodynamic variables (P, V, T) of the system is called an equation of state.

For n moles of an ideal gas, the equation of state is PV = nRT

For n moles of a real gas equation of state is $\left(P+\frac{a n^2}{V^2}\right)(V-n b)=n R T$

Thermodynamic process: The process of change of state of a system involves a change of thermodynamic variables such as pressure P, volume V, and temperature T of the system. The process is known as the thermodynamic process.

Some important processes are -

(i) Isothermal process (ii) Adiabatic process (iii) Isobaric process (iv) Isochoric process

(v) Cyclic and non-cyclic process (vi) Reversible and irreversible process

Later, we will study all these processes one by one in detail.

State or Point function does not depend on the path followed by the thermodynamic process but it depends on the final and initial position of the process.

Path function depends on the path followed by a thermodynamic process and not on the initial and final states of the system. An example of a point function is Internal energy and an example of a path function is Heat and work.