Thermodynamics

For one mole of an ideal gas, which of these statements must be true?

$\mathrm{U}$ and $\mathrm{H}$ each depends only on temperature

Compressibility factor $z$ is not equal to 1

${\mathrm{C}}_{\mathrm{P},\mathrm{m}}-{\mathrm{C}}_{\mathrm{v},\mathrm{m}}=\mathrm{R}$

$\mathrm{d}\mathrm{U}={\mathrm{C}}_{\mathrm{V}}\mathrm{d}\mathrm{T}$ for any process

A closed vessel contains 0.1 mole of a monatomic ideal gas at $200\mathrm{K}$ . If 0.05 mole of the same gas at $400\mathrm{K}$ is added to it, the final equilibrium temperature (in $\mathrm{K}$ ) of the gas in the vessel will be close to

4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 20L. The amount of heat absorbed in this expansion is _________L atm.

For a transverse wave traveling along a straight line, the distance between two peaks (crests) is 5
 , while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in $\mathrm{A}\to \mathrm{I}\mathrm{V};\mathrm{}\mathrm{B}\to \mathrm{I}$ ) of the waves are:

The specific heat of water $=4200\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ and the latent heat of ice $=3.4\times {10}^5\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}$ . 100 grams of ice at $0^{\circ }\mathrm{C}$ is placed in $200\mathrm{g}$ of water at ${25}^{\circ }\mathrm{C}$ . The amount of ice that will melt as the temperature of water reaches $0^{\circ }\mathrm{C}$ is close to (in grams):

A beam of plane polarized light of large cross-sectional area and uniform intensity of $3.3{\mathrm{W}\mathrm{m}}^{-2}$ falls normally on a polarizer (cross sectional area $3\times {10}^{-4}{\mathrm{m}}^2$ ) which rotates about its axis with an angular speed of $31.4\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}$ . The energy of light passing through the polariser per revolution, is close to:

The total internal energy of two mole mono atomic ideal gas at temperature T = 300K will be __________J. (Given R = 8.31 J/mol.K)

Given below are two statements:

Statement – I : When $\mu$ <!-- [if gte mso 9]><xml> </xml><![endif]-->moment of an ideal gas undergoes adiabatic change from state <!-- [if gte mso 9]><xml> </xml><![endif]-->  $\left(P_1,V_1,T_1\right)$ to state $\left(P_2,V_2,T_2\right)$ <!-- [if gte mso 9]><xml> </xml><![endif]--> then work done is w = $\frac{\mu R\left(T_2-T_1\right)}{1-\gamma },$ <!-- [if gte mso 9]><xml> </xml><![endif]--> where <!-- [if gte mso 9]><xml> </xml><![endif]--> $\gamma =\frac{C_p}{C_v}and$ R = universal gas constant.

Statement – II : In the above case, when work done on the gas, the temperature of the gas would rise.

Choose the correct answer from the options given below:

Five moles of an ideal gas at 1 bar and $298\mathrm{K}$ is expanded into vacuum to double the volume. The work done is :

The process that is NOT endothermic in nature is: