Thermodynamics practice · Mixed difficulty

Statement-I: Two vessels A and B are connected to each other by a stopcock. Vessel A contains a gas at $300 \mathrm{~K}$ and 1 atmosphere pressure and vessel B is evacuated. The two vessels are thermally insulated from the surroundings. If the stopcock is suddenly opened, the expanding gas does no work.
Statement-II: Since $\Delta Q=0$ and as the gas expands freely so $\Delta W=0$ and from the first law of thermodynamics it follows that $\Delta U$ is also zero for the above process.

$n_1$ and $n_2$ are the moles of two ideal gases, whose thermodynamics constants, [ratio of $\left(\frac{C_p}{C_v}\right)$ ] are $\gamma_1$ and $\gamma_2$ respectively, are mixed. $\left(\frac{C_p}{C_v}\right)$ for the mixture is-

A gas mixture consists of 4 moles of $\mathrm{O}_2$ and 8 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

If a gas is compressed adiabatically by doing work of $250 \mathrm{~J}$, the change in intemal energy of the gas is:

When a body A is in thermal equilibrium with a body B, and also separately with a body C, then B and C will be in thermal equilibrium with each other.

$10 \mathrm{~g}$ of water at $30^{\circ} \mathrm{C}$ and $10 \mathrm{~g}$ of ice at $-20^{\circ} \mathrm{C}$ are mixed together in a calorimeter. Find the amount of ice that melts. (Specific heat of ice $=0.5 \mathrm{~cal} \mathrm{~g}^{-1}{ }^{\circ} \mathrm{C}$ ${ }^1$ and latent heat of ice $=80 \mathrm{~cal} \mathrm{~g}^{-1}$ ).

Which of the following processes is reversible

Two identical containers $X$ and $Y$ with friction less pistons contain the same ideal gas at the same temperature and the same volume $V$. The mass of gas $X$ is $m_x$ and that of $Y$ is $m_y$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2 V$. The change in the pressure in $X$ and $Y$ are found to be $\Delta P$ and $3 \Delta P$ respectively. Then,

When an ideal gas $\left( {\gamma = 5/3} \right)$ is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work

The work done during expansion of a gas is independent of pressure if the expansion takes place

A Carnot engine has efficiency of $50 \%$. If the temperature of sink is reduced by $40^{\circ} \mathrm{C}$, its efficiency increases by $30 \%$. The temperature of the source will be:

Two Carnot engines A and B are operated in series. The engine $A$ receives heat from the source at temperature $T_1$ and rejects the heat to the sink at temperature $\mathrm{T}$. The second engine $B$ receives the heat at temperature $T$ and rejects to its sink at temperature $T_2$. For what value of $T$ the efficiencies of the two engines are equal?

First law of thermodynamics is based on

The efficiency of the Carnot engine is $50 \%$ and the temperature of the sink is $500 {~K}$. If the temperature of the source is kept constant and its efficiency raised to $60 \%$, then the required temperature of the sink will be

(A): $Q$ heat is given to melt ice cube and magnitude of work done by ice on surrounding is $W.$ then $\Delta Q=Q-W$
(R): First law of thermodynamics is applicable in this situation.

Assertion: The internal energy of a real gas is function of both, temperature and volume.
Reason: At constant pressure, some heat is spent in expansion of the gas.

Assertion(A): In adiabatic expansion process, the product of $p$ and $V$ always decreases.

Reason(R): In adiabatic expansion process, work is done by the gas at the cost of internal energy of gas.

During an adiabatic compression, 830 J of work is done on 2 moles of a diatomic ideal gas to reduce its volume by 50%. The change in its temperature is nearly: ($R = 8.3\,J{K^{ - 1}}\,mo{l^{ - 1}}$)

A process is said to be reversible if

Assertion: The efficiency of a reversible engine is maximum
Reason: In such a device no dissipation of energy takes place.

The work done in an isothermal expansion of a gas depends upon

Work done by 0.1 mole of a gas at ${27^ \circ }C$ to double its volume at constant pressure is $\left( {R = 2\;cal\;mo{l^{ - 1}}\,\,^\circ {C^{ - 1}}} \right)$

Assertion: Sum of two path functions is always a path function.
Reason: Every state function can be produced by path functions.

A mass $m$ of lead shot is placed at the bottom of a vertical cardboard cylinder that is $1.5 \mathrm{~m}$ long and closed at both ends. The cylinder is suddenly inverted so that the shot falls $1.5 \mathrm{~m}$. If this process is repeated quickly 100 times, assuming no heat is dissipated or lost, the temperature of the shot will increase by (specific heat of lead $=0.03 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}$ )

An ideal heat engine works between temperatures ${T_1} = 500\mathrm{K and}{T_2} = 375\mathrm{K}$. If the engine absorbs 600 J of heat from the source, then the amount of heat released to the sink is

In an isothermal process the volume of an ideal gas is halved. One can say that

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

A hammer of mass '$1$' $kg$ having speed of $50\,m/s$, hit a iron nail of mass $200\,gm$. If specific heat of
iron is $0.105\,\,cal/g{m^0}C$ and half the energy is converted into heat, the raise be temperature of nail is

Assertion: For an isothermal process in an ideal gas, the heat obsorbed by the gas is entirely used in the work done by the gas.
Reason: During a process taking place in a system, the temperature remains constant then the process is isothermal.

In a $p - V$ diagram for an ideal gas (where $p$ is along $y$-axis and $V$ is along $x$-axis), the value of the ratio "slope of adiabatic curve/slope of the isothermal curve" at any point will be (where symbols have their usual meanings).