Embibe Experts Solutions for Chapter: Thermodynamics, Exercise 5: Exercise-5

Two moles of an ideal gas are heated at a constant pressure of one atmosphere from $27°\mathrm{C}$ to $127°\mathrm{C}$. If ${\mathrm{C}}_{\mathrm{v},\mathrm{m}}=20+{10}^{-2}{\mathrm{TJK}}^{-1}{\mathrm{mol}}^{-1},$ $\mathrm{q}$ and $\Delta \mathrm{U}$ for the process are, respectively:

Consider a classroom that is roughly $5\mathrm{m}\times 10\mathrm{m}\times 3\mathrm{m}.$ Initially, $\mathrm{t}=27°\mathrm{C}$ $\mathrm{P}=1$ atm. There are $50$ people in an insulated class losing energy to the room at the average rate of $150$ Watt per person. How long can they remain in the class if the body temperature is $42°\mathrm{C}$ and the person feels uncomfortable above this temperature? Heat capacity of air$=(7/2)\mathrm{R}$.

There are two samples of the same gas, initially under the similar initial state. Gases of both the samples are expanded. ${\mathrm{I}}^{\text{st }}$ sample using reversible isothermal process and ${\mathrm{II}}^{\text{nd }}$ sample using reversible adiabatic process till the final pressures of both the samples becomes half of the initial pressure. Then:

In a laboratory, liquid in a thermally insulated container is stirred for one hr, by a mechanical linkage to an in the surrounding, for this process:

The efficiency of an hypothetical cell is about $84\%$ which involves the following reaction:

$\mathrm{A}\left(\mathrm{s}\right)+{\mathrm{B}}^{2+}\left(\mathrm{aq}\right)⟶{\mathrm{A}}^{2+}\left(\mathrm{aq}\right)+\mathrm{B}\left(\mathrm{s}\right); \mathrm{\Delta H}=-285 \mathrm{kJ}$

Then, the standard electrode potential of the cell will be (Assume as $\mathrm{\Delta S}=0$)

The temperature coefficient, of the emf i.e. $\frac{\mathrm{dE}}{\mathrm{dT}}=-0.00065 \mathrm{volt} {\mathrm{deg}}^{-1}$ for the cell $\mathrm{Cd}\overline{){\mathrm{CdCl}}_2\left(1 \mathrm{M}\right)}\Vert \mathrm{AgCl}\left(\mathrm{s}\right)|\mathrm{Ag}$ at $25°\mathrm{C}$. Calculate the entropy changes ${\mathrm{\Delta S}}_{298 \mathrm{K}}$ for the cell reaction, $\mathrm{Cd}+2\mathrm{AgCl}\to {\mathrm{Cd}}^{++}+2{\mathrm{Cl}}^{-}+2\mathrm{Ag}$

The potential of the Daniell cell, $\mathrm{Zn}\left|\begin{array}{c}{\mathrm{ZnSO}}_4\\ \left(1 \mathrm{M}\right)\end{array}\right|\left|\begin{array}{c}{\mathrm{CuSO}}_4\\ \left(1 \mathrm{M}\right)\end{array}\right|\mathrm{Cu}$ was reported by Buckbee, Surdzial and Metz as $\mathrm{E}°=1.1028-0.641\times {10}^{-3}\mathrm{T}+0.72\times {10}^{-5}{\mathrm{T}}^2$, where, $\mathrm{T}$ is the temperature in degree celsius. Calculate $\mathrm{\Delta S}°$ for the cell reaction at $25°\mathrm{C}$:

$\mathrm{\Delta G}=\mathrm{\Delta H}-\mathrm{T\Delta S}$ and $\mathrm{\Delta G}=\mathrm{\Delta H}+\mathrm{T}{\left[\frac{\mathrm{d}\left(\mathrm{\Delta G}\right)}{\mathrm{dT}}\right]}_{\mathrm{p}}$ then $\left(\frac{{\mathrm{dE}}_{\mathrm{cell}}}{\mathrm{dT}}\right)$ is :