The enthalpy change $\left( \Delta H \right)$ for the reaction,$N_{2(g)} + 3H_{2(g)} \to 2NH_{3(g)}$ is $-92.38 \ kJ$ at $298 \ K$. The internal energy change $\left( \Delta U \right)$ at $298 \ K$ is ........ $kJ$.

There is a uniform electric field of strength $10^3 \ Vm^{-1}$ along the $Y$-axis. $A$ body of mass $1 \ g$ and charge $10^{-6} \ C$ is projected into the field from the origin along the positive $X$-axis with a velocity of $10 \ ms^{-1}$. Its speed in $ms^{-1}$ after $10 \ s$ is (Neglect gravitation).

In a reaction,$A + B \rightleftharpoons C + D$,$40 \%$ of $B$ has reacted at equilibrium,when $1 \ mole$ of $A$ was heated with $1 \ mole$ of $B$ in a $10 \ L$ closed vessel. The value of $K_C$ is

The minimum force required to start pushing a body up a rough (frictional coefficient $\mu$) inclined plane is $F_1$,while the minimum force needed to prevent it from sliding down is $F_2$. If the inclined plane makes an angle $\theta$ with the horizontal such that $\tan \theta = 2 \mu$,then the ratio $\frac{F_1}{F_2}$ is:

Which of the following statements is incorrect?

For all values of $\theta$,the values of $3-\cos \theta+\cos \left(\theta+\frac{\pi}{3}\right)$ lie in the interval :