One mole of an ideal gas is taken from $\mathbf{a}$ to $\mathbf{b}$ along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is $W_{\text {s }}$ and that dotted line path is $W_{\mathrm{d}}$, then the integer closest to the ratio $W_{\mathrm{d}} / W_{\mathrm{s}}$ is

In a constant volume calorimeter, 3.5 g of a gas with molecular weight 28 was burnt in excess oxygen at 298.0 K. The temperature of the calorimeter was found to increase from 298.0 K to 298.45 K due to the combustion process. Given that the heat capacity of the calorimeter is 2.5 kJ K$$^{-1}$$, the numerical value for the enthalpy of combustion of the gas in kJ mol$$^{-1}$$ is ____________.

For the reaction, $2 \mathrm{CO}+\mathrm{O}_2 \rightarrow 2 \mathrm{CO}_2 ; \Delta \mathrm{H}=-560 \mathrm{~kJ}$. Two moles of CO and one mole of $\mathrm{O}_2$ are taken in a container of volume 1 L . They completely form two moles of $\mathrm{CO}_2$, the gases deviate appreciably from ideal behaviour. If the pressure in the vessel changes from 70 to 40 atm , find the magnitude (absolute value) of $\Delta \mathrm{U}$ at 500 K . $(1 \mathrm{~L} \mathrm{~atm}=0.1 \mathrm{~kJ})$