$7$ mole of certain monoatomic ideal gas undergoes a temperature increase of $40 \mathrm{K}$ at constant pressure. The increase in the internal energy of the gas in this process is
(Given $R=8.3 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$)

Read the following statements :
$\mathrm{A}$. When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice.

$\mathrm{B}$. Two bodies $P$ and $Q$ having equal surface areas are maintained at temperature $10°\mathrm{C}$ and $20°\mathrm{C}$. The thermal radiation emitted in a given time by $P$ and $Q$ are in the ratio $1:1.15$

$\mathrm{C}$. A carnot Engine working between $100 \mathrm{K}$ and $400 \mathrm{K}$ has an efficiency of $75\%$

$\mathrm{D}$. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.

Choose the correct answer from the options given below :

In $1^{\mathrm{st}}$${ }^{}$ case, Carnot engine operates between temperatures $300 \mathrm{K}$ and $100 \mathrm{K}$. In $2^{\mathrm{nd}}$${ }^{}$ case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in $2^{\mathrm{nd}}$${ }^{}$ case) will be :

The pressure $P_1$ and density $d_1$ of diatomic gas $\left(\gamma =\frac{7}{5}\right)$ changes suddenly to $P_2\left(>P_1\right)$ and $d_2$ respectively during an adiabatic process. The temperature of the gas increases and becomes____times of its initial temperature. 

(Given $\frac{d_2}{ d_1}=32$)

A thermodynamic system is taken from an original state $D$ to an intermediate state $E$ by the linear process shown in the figure. Its volume is then reduced to the original volume from $E$ to $F$ by an isobaric process. The total work done by the gas from $D$ to $E$ to $F$ will be