If the r. m.s speed of chlorine molecule is $$490\mathrm{m}/\mathrm{s}$$ at $$27^{\circ }\mathrm{C}$$, the r. m. s speed of argon molecules at the same temperature will be (Atomic mass of argon $$=39.9\mathrm{u}$$, molecular mass of chlorine $$=70.9\mathrm{u}$$ )

The Thermodynamic process, in which internal energy of the system remains constant is

The root mean square speed of molecules of nitrogen gas at $$27^{\circ }\mathrm{C}$$ is approximately : (Given mass of a nitrogen molecule $$=4.6\times 10^{-26}\mathrm{kg}$$ and take Boltzmann constant $${\mathrm{k}}_{\mathrm{B}}=1.4\times 10^{-23}{\mathrm{JK}}^{-1}$$ )

$$1\mathrm{kg}$$ of water at $$100^{\circ }\mathrm{C}$$ is converted into steam at $$100^{\circ }\mathrm{C}$$ by boiling at atmospheric pressure. The volume of water changes from $$1.00\times 10^{-3}{\mathrm{m}}^3$$ as a liquid to $$1.671{\mathrm{m}}^3$$ as steam. The change in internal energy of the system during the process will be (Given latent heat of vaporisaiton $$=2257\mathrm{kJ}/\mathrm{kg}$$, Atmospheric pressure = $$1\times 10^5\mathrm{Pa})$$

On a temperature scale '$$\mathrm{X}$$', the boiling point of water is $$65^{\circ }\mathrm{X}$$ and the freezing point is $$-15^{\circ }\mathrm{X}$$. Assume that the $$\mathrm{X}$$ scale is linear. The equivalent temperature corresponding to $$-95^{\circ }\mathrm{X}$$ on the Farenheit scale would be:

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the basis of their root mean square speed $$\left(v_{\mathrm{rms}}\right)$$ and choose the correct answer from the options given below:

A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,

A gas is compressed adiabatically, which one of the following statement is NOT true.

Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas in A is compressed isothermally to $$\frac{1}{8}$$ of its original volume while the gas in B is compressed adiabatically to $$\frac{1}{8}$$ of its original volume. The ratio of final pressure of gas in B to that of gas in A is

Match List I with List II : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-baqh{text-align:center;vertical-align:top} .tg .tg-amwm{font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0lax{text-align:left;vertical-align:top} List I List II (A) 3 Translational degrees of freedom (I) Monoatomic gases (B) 3 Translational, 2 rotational degrees of freedoms (II) Polyatomic gases (C) 3 Translational, 2 rotational and 1 vibrational degrees of freedom (III) Rigid diatomic gases (D) 3 Translational, 3 rotational and more than one vibrational degrees of freedom (IV) Nonrigid diatomic gases Choose the correct answer from the options given below:

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at $$27^{\circ }\mathrm{C}$$ is

Work done by a Carnot engine operating between temperatures $$127^{\circ }\mathrm{C}$$ and $$27^{\circ }\mathrm{C}$$ is $$2\mathrm{kJ}$$. The amount of heat transferred to the engine by the reservoir is :

Given below are two statements: Statement I: If heat is added to a system, its temperature must increase. Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase. In the light of the above statements, choose the correct answer from the options given below

A source supplies heat to a system at the rate of $$1000\mathrm{W}$$. If the system performs work at a rate of $$200\mathrm{W}$$. The rate at which internal energy of the system increases is

The number of air molecules per cm$${}^3$$ increased from $$3\times 10^{19}$$ to $$12\times 10^{19}$$. The ratio of collision frequency of air molecules before and after the increase in number respectively is:

The temperature of an ideal gas is increased from $$200\mathrm{K}$$ to $$800\mathrm{K}$$. If r.m.s. speed of gas at $$200\mathrm{K}$$ is $$v_0$$. Then, r.m.s. speed of the gas at $$800\mathrm{K}$$ will be:

A body cools in 7 minutes from $$60^{\circ }\mathrm{C}$$ to $$40^{\circ }\mathrm{C}$$. The temperature of the surrounding is $$10^{\circ }\mathrm{C}$$. The temperature of the body after the next 7 minutes will be:

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

Considering a group of positive charges, which of the following statements is correct ?

Let $$\sigma$$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region $$E_I,E_{II}$$ and $$E_{III}$$ are: