Thermodynamics practice · Mixed difficulty

One gram of water (volume $=1 \mathrm{~cm}^3$ ) becomes 1671 $\mathrm{cm}^3$ of steam when boiled at a pressure of one atmosphere . Latent heat of vaporization at this pressure is $539 \mathrm{~cal} / \mathrm{gm}$. Compute the work done. $\left[1 \mathrm{~atm}=1.013 \times 10^5 \mathrm{Nm}^{-2}\right.$ ]

Identify the characteristics of an adiabatic process in a monoatomic gas.

(A) Internal energy is constant.

(B) Work done in the process is equal to the charge in internal energy.

(C) The product of temperature and volume is a constant.

(D) The product of pressure and volume is a constant.

(E) The work done to change the temperature from $\mathrm{T}_1$ to $\mathrm{T}_2$ is proportional to $\left(\mathrm{T}_2-\mathrm{T}_1\right)$

Choose the correct answer from the options given below:

Choose the correct statement

The slopes of isothermal and adiabatic curves are related as

Assertion: The efficiency of a heat engine can be unity.
Reason: Efficiency of heat engine is fundamental limitation given by first law of thermodynamics.

Statement-I: Monoatomic, diatomic and polyatomic gases are adiabatically compressed such that compression ratio is $\left(\frac{P_2}{P_1}\right)$. Then monoatomic gas will have maximum final volume out of these three gases.
Statement-II: Monoatomic gas has least degree of freedom.

A carnot engine takes $3 \times {10^6}\,\,cal$ of heat from a reservoir at ${627^0}C$ and gives it to a sink at ${27^0}C$. The work done by the engine is,

The relation between two specific heats of a gas is

One mole of oxygen is expanded from a volume $1 \mathrm{~L}$ to $5 \mathrm{~L}$ at a constant temperature $T=280 \mathrm{~K}$. The change in internal energy is:

An ideal gas A and a real gas B have their volumes increased from V to 2V under isothermal conditions. The increase in internal energy

(A): A room can not be cooled by opening the door of a refrigerator in a closed room
(R): Heat flows from lower temperature (refrigerator) to higher temperature (room).

In thermodynamics, heat and work are:

The specific heat of an ideal gas for an isothermal process is

An engine is supposed to operate between two reservoirs at temperature ${727^0}C\,\,and\,\,{227^0}C$ . The maximum possible efficiency of such an engine is

The internal energy of an ideal gas increases during an isothermal process when the gas is

The molar specific heat at constant pressure for a monoatomic gas is

$n$ moles of an ideal gas with constant volume heat capacity ${C_V}$ undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is

Assertion: A heat engine is the reverse of a refrigerator.
Reason: A refrigerator cannot work without some external work done on the system.

(A): An adiabatic process is an isoentropic process.
(R): Change in entropy is zero in case of adiabatic process.

An ideal gas in a piston cylinder arrangement is to be taken from a temperature of $500 {~K}$ to a temperature of $600 {~K}$. Which of the thermodynamic process given in options should be used so that the final state of $600 {~K}$ is achieved using a minimum energy input from outside?

The change of entropy, when heat is absorbed by the gas is:

In a Carnot engine, when ${T_2} = 0\,^\circ C\,\,\,\mathrm{and}\;\,\,{T_1} = 200\,^\circ C$ its efficiency is  ${\mathrm{\eta }_1}\mathrm{\;}\,\,\mathrm{and\;}\,\,\,\mathrm{when}\;\,\,\,{T_1} = 0\,^\circ C\;\,\,\mathrm{and}\,\,\;{T_2} = - 200\,^\circ C\;,$ its efficiency is ${\mathrm{\eta }_2}$, then what in ${\eta _1}/{\eta _2}?$

The theory of refrigerator is based on

An engine takes in compressed steam at ${127^ \circ }C$ and rejects it at ${47^ \circ }C$ . Efficiency of the engine is

In which of the processes, does the internal energy of the system remain constant?

The $\Delta H_f^{\circ}$ for $\mathrm{CO}_2(\mathrm{~g}), \mathrm{CO}(\mathrm{g})$ and $\mathrm{H}_2 \mathrm{O}(\mathrm{g})$ are $-393.5,-110.5$ and $-241.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. The standard enthalpy change (in $\mathrm{kJ}$ ) for the reaction,
$\mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})$ is

In an isobaric process, $\Delta Q=\frac{\gamma K}{\gamma-1}$, where $\gamma$ is $\boldsymbol{C}_{\boldsymbol{p}} / \boldsymbol{C}_{\boldsymbol{v}}$ What is $K$ ?

An ideal gas at pressure $2.5 \times 10^5 \mathrm{~Pa}$ and temperature $300 \mathrm{~K}$ occupies $100 \mathrm{cc}$. It is adiabatically compressed to half its original volume. Calculate (a) the final temperature and (b) the work done by the gas in the process. Take $\gamma=1.5$.

The work done, W during an isothermal process in which 1 mole of the gas expands from an initial volume ${V_1}$to a final volume ${V_2}$ is given by (R=gas constant, T=temperature)

In an isothermal expansion