The rate constant is doubled when temperature increases from $27^{\circ} C$ to $37^{\circ} C$. What is the activation energy in $kJ \ mol^{-1}$?

For a first order reaction $A \rightarrow P$,the temperature $(T)$ dependent rate constant $(k)$ was found to follow the equation $\log_{10} k = -(2000) \frac{1}{T} + 6$. The activation energy $(E_a)$ of the reaction in $kJ \, mol^{-1}$ will be ......... (Given: $\ln x = 2.3 \times \log_{10} x$ and $R = 8 \, J \, mol^{-1} K^{-1}$)

The rate of a reaction quadruples when the temperature changes from $293 \ K$ to $313 \ K$. Calculate the energy of activation of the reaction assuming that it does not change with temperature.

For the decomposition reaction of $N_2O_5$,the slope of the graph of $\log K$ versus $1/T$ is $-1.2 \times 10^4 \ K$. Calculate the activation energy $(E_a)$ of the reaction.

Consider the given energy profile diagram for a reaction and choose the correct option:

$A$ student determined the value of the rate constant,$k$,for a chemical reaction at several different temperatures. Which of the following graphs of the student's data would give a straight line?