Let $f$ be a positive function. Let $I_1 = \int_{1-k}^{k} x f\{x(1-x)\} dx$ and $I_2 = \int_{1-k}^{k} f\{x(1-x)\} dx$,where $2k-1 > 0$. Then $I_1/I_2$ is

$A$ reversible engine converts one-sixth of the heat supplied into work. When the temperature of the sink is reduced by $62^{\circ} C$,the efficiency of the engine is doubled. The temperatures of the source and sink are

Consider the following statements $A$ and $B$ and identify the correct answer given below.
$A$. Peltier coefficient is numerically equal to the potential difference across the junctions of the thermocouple through which current is flowing.
$B$. According to Thomson,energy is neither absorbed nor evolved at the junction of a thermocouple but is absorbed or evolved only along the lengths of both the conductors.

The solution of the differential equation $x y^2 d y - (x^3 + y^3) d x = 0$ is

The chemical reaction that involves the roasting process is

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and then is compressed to the original volume $V_1$ adiabatically. The initial pressure is $P_1$ and the final pressure is $P_3$. The total work done is $W$. Then: