$A$ gas is governed by an equation $V = \frac{aT^3}{P}$,where $P, V$,and $T$ are pressure,volume,and temperature of the gas respectively,and $a$ is a constant. If the temperature of the gas is doubled at constant pressure,then the work done by the gas is: (in $aT^3$)

Carbon monoxide is carried around a closed cycle $abc$ in which $bc$ is an isothermal process as shown in the figure. The gas absorbs $7000 \; J$ of heat as its temperature increases from $300 \; K$ to $1000 \; K$ in going from $a$ to $b$. The quantity of heat rejected by the gas during the process $ca$ is ..... $J$. (in $; J$)

The ratio of the slopes of isothermal and adiabatic curves is

Which of the following statement$(s)$ is/are true? "Internal energy of an ideal gas ..........."

Select the correct statement for work, heat, and change in internal energy.

Fill in the blanks:
$1.$ The change of internal energy in a cyclic process is ......
$2.$ The internal energy of a gas is increased by ......
$3.$ An ideal gas at temperature $T_1$ is compressed to $1/32$ of its original volume,then its temperature $T_2$ will be ...... $(\gamma = 1.4)$.
$4.$ The triple point of water is at ...... pressure and ...... temperature.