Statement = $C_P-C_V=R$ for an ideal gas

Explanation $={\left(\frac{\partial U}{\partial V}\right)}_T=0$ for an ideal gas.

The molar heat capacity for an ideal gas at constant pressure is $20.785 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$. The change in internal energy is $5000 \mathrm{J}$ upon heating it from $300 \mathrm{K}$ to $500 \mathrm{K}$. The number of moles of the gas at constant volume is____

(Given: $\mathrm{R}=8.314 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$)

The specific heat of a certain substance is $0.86 \mathrm{J} {\mathrm{g}}^{-1} {\mathrm{K}}^{-1}$. Assuming ideal solution behavior, the energy required (in $\mathrm{J}$) to heat $10 \mathrm{g}$ of $1$ molal of its aqueous solution from $300 \mathrm{K}$ to $310 \mathrm{K}$ is closest to :

[Given: molar mass of the substance $=58 \mathrm{g} {\mathrm{mol}}^{-1}$; specific heat of water $=4.2 \mathrm{J} {\mathrm{g}}^{-1} {\mathrm{K}}^{-1}$]

$\mathrm{A}$ fish swimming in water body when taken out from the water body is covered with a film of water of weight $36 \mathrm{g}$. When it is subjected to cooking at $100 °\mathrm{C}$, then the internal energy for vaporization in ${\mathrm{kJmol}}^{-1}$ is integer]

[Assume steam to be an ideal gas. Given ${\mathrm{\Delta }}_{\mathrm{vap}}{\mathrm{H}}^{\ominus }$ for water at $373 \mathrm{K}$ and $1$ bar is $41.1 \mathrm{kJ}{ \mathrm{mol}}^{-1}:\mathrm{R}=8.31 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$]

The quantity of heat (in $J$) required to raise the temperature of $1.0\mathit{ }kg$ of ethanol from $293.45 K$ to the boiling point and then change the liquid to vapor at that temperature is closest to [Given, boiling point of ethanol $351.45 K$. Specific heat capacity of liquid ethanol $2.44\mathit{ }J\mathit{ }{g}^{-1} K^{-1}$. Latent heat of vaporisation of ethanol $855 J{g}^{-1}$ ]

The combination of plots which does not represent isothermal expansion of an ideal gas is

$\left(\mathrm{A}\right)$

$\left(\mathrm{B}\right)$

$\left(\mathrm{C}\right)$

$\left(\mathrm{D}\right)$

$200 \mathrm{mL}$ of $0.2 \mathrm{M} \mathrm{HCl}$ is mixed with $300 \mathrm{mL}$ of $0.1 \mathrm{M} \mathrm{NaOH}.$ The molar heat of neutralization of this reaction is $-57.1 \mathrm{kJ}.$ The increase in temperature in ${}^{\circ }\mathrm{C}$ of the system on mixing is $\mathrm{x}\times {10}^{-2}.$ The value of $\mathrm{x}$ is (Nearest integer)

[Given: Specific heat of water $=4.18 \mathrm{J} {\mathrm{g}}^{-1} {\mathrm{K}}^{-1}$ 

Density of water$=1.00 \mathrm{g}{ \mathrm{cm}}^{-3}$]

(Assume no volume change on mixing)