thermodynamics Questions

A Carnot engine has an efficiency of $50\%$ when its source is at a temperature $327^{\circ }\text{C}$. The temperature of the sink is:

The temperature of gas is $-50^{\circ }\text{C}$. To what temperature the gas should be heated so that the RMS speed is increased by $3$ times?

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R:Assertion A: In the equation ${\Delta }_{r}G=-nF{E}_{cell}$, the value of ${\Delta }_{r}G$ depends on $n$.Reason R: $E_{cell}$ is an intensive property and ${\Delta }_{r}G$ is an extensive property.In the light of the above statements, choose the correct answer:

Which amongst the following options is the correct relation between change in enthalpy and change in internal energy?

The equilibrium concentrations of the species in the reaction $\text{A}+\text{B}\rightleftharpoons \text{C}+\text{D}$ are $2,3,10$ and $6{\text{mol L}}^{-1}$, respectively at $300\text{K}$. $\Delta G^{\circ }$ for the reaction is ($R=2\text{cal/mol K}$):