Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$ , while box $B$ contains one mole of helium at temperature $(7/3)\, T_0$ . The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes), then the final temperature of gases $T_f$ , in terms of $T_0$ is

An ideal gas heat engine operates in Carnot's cycle between $227\,^oC$ and $127\,^oC$ . It absorbs $6.0 \times 10^4\,cal$ at higher temperature. The amount of heat converted into work is equal to

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 $T$. 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?

An ideal gas is expanding such that $PT^2 =$ constant. The coefficient of volume expansion of the gas is

$1\  cc$ of water at its boiling point $(100^o\  C)$ is converted into steam by supplying it $540\  calories$ of heat the volume of steam is $1671\  cc$. If atmospheric pressure is $1.013 × 10^ 5\  Nm^{-2}$ and $J = 4.18\  joule/cal$ the approximate value of heat that is required in overcoming the molecular attraction is …….. $cal$