A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by :-
 

Helium gas goes through a cycle $ABCDA$ (consisting of two isochoric and isobaric lines) as shown in the figure. The efficiency of this cycle is nearly (assume the gas to be close to ideal gas) 

A carnot engine, whose efficiency is $40\%$, takes in heat from a source maintained at a temperature of $500 \mathrm{K}$. It is desired to have an engine of efficiency $60\%$. Then, the intake temperature for the same exhaust (sink) temperature must be

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

One mole of diatomic ideal gas undergoes a cyclic process $ABC$ as shown in the figure. The process $BC$ is adiabatic. The temperature at $A, B$ and $C$ are $400 \mathrm{K}$, $800 \mathrm{K}$ and $600 \mathrm{K}$, respectively. Choose the correct statement.

A solid body of constant heat capacity $1 \mathrm{J} {}^{\circ }\mathrm{C}^{-1}$ is being heated by keeping it in contact with reservoirs in two ways
(i) Sequentially keeping in contact with $2$ reservoirs such that each reservoir supplies the same amount of heat.
(ii) Sequentially keeping in contact with $8$ reservoirs such that each reservoir supplies the same amount of heat.

In both the cases, the body is brought from initial temperature $100 °\mathrm{C}$ to final temperature $200 °\mathrm{C}$. Entropy change of the body in the two cases respectively, is

A gas can be taken from $A$ to $B$ via two different processes $ACB$ and $ADB$. When path $ACB$ is used $60 \mathrm{J}$ of heat flows into the system and $30 \mathrm{J}$ of work is done by the system. If path $ADB$ is used work done by the system is $10 \mathrm{J}$. The heat flow into the system in path $ADB$ is