The heat energy that must be supplied to $14 \text{ g}$ of nitrogen at room temperature to raise its temperature by $48^{\circ}C$ at constant pressure is ($R$ = gas constant, Molecular weight of nitrogen $(N_2) = 28$) (in $R$)

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 the boxes). The final temperature of the gases,$T_f$,in terms of $T_0$ is:

Two thermally insulated vessels $1$ and $2$ contain air at temperatures $(T_1, T_2)$,volumes $(V_1, V_2)$,and pressures $(P_1, P_2)$. If the valve connecting them is opened,what will be the equilibrium temperature of the system?

In saloons,there is always a characteristic smell due to the ammonia-based chemicals used in hair dyes and other products. Assume the initial concentration of ammonia molecules to be $1000 \text{ molecules}/m^3$. Due to air ventilation,the number of molecules leaving in one minute is one-tenth of the molecules present at the start of that minute. How long will it take for the concentration of ammonia molecules to reach $1 \text{ molecule}/m^3$?

$A$ hot air balloon with a payload rises in the air. Assume that the balloon is spherical in shape with a diameter of $11.7 \, m$ and the mass of the balloon and the payload (without the hot air inside) is $210 \, kg$. The temperature and pressure of the outside air are $27^{\circ} C$ and $1 \, atm = 10^5 \, N/m^2$,respectively. The molar mass of dry air is $30 \, g/mol$. The temperature of the hot air inside is close to .......... $^{\circ} C$. [The gas constant,$R = 8.31 \, J K^{-1} mol^{-1}$]

The difference between volume and pressure coefficients of an ideal gas is