When $Q_1$ amount of heat is supplied to a monatomic gas, the work done by the gas is $W$. When $Q_2$ amount of heat is supplied to a diatomic gas, the work done by the gas is $2W$. Then $Q_1: Q_2=$

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

The slopes of isothermal and adiabatic curves are related as

Consider the following statements:
$A$. Zeroth law of thermodynamics gives the concept of temperature.
$B$. First law of thermodynamics gives the concept of internal energy.
$C$. In isothermal expansion of an ideal gas, $\Delta Q \neq \Delta W$.
$D$. The product of intensive and extensive variables is extensive.
$E$. The ratio of any extensive variable to mass will be an extensive variable.
Choose the correct combination of statements from the options given below:

$A$ cylinder made of perfectly non-conducting material,closed at both ends,is divided into two equal parts by a heat-proof piston. Both parts of the cylinder contain the same mass of a gas at a temperature $t_0 = 27^{\circ}C$ and pressure $P_0 = 1 \text{ atm}$. If the gas in one of the parts is slowly heated to $t = 57^{\circ}C$ while the temperature of the first part is maintained at $t_0$,the distance moved by the piston from the middle of the cylinder will be $x \text{ cm}$. Find $x$ (total length of the cylinder $= 84 \text{ cm}$).

An ideal monoatomic gas is carried along the cycle $ABCDA$ as shown in the figure. The total heat absorbed during this process is (in $p_0 V_0$)