A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm3 to 150 cm3 adiabatically. In this process, the value of workdone on the gas will be :

A certain amount of gas of volume $$\mathrm{V}$$ at $$27^{\circ }\mathrm{C}$$ temperature and pressure $$2\times 10^7{\mathrm{Nm}}^{-2}$$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $$\gamma =1.5)$$ :

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $$\sqrt{2}$$ times the speed of sound, then the value of n will be :

Let $${\eta }_1$$ is the efficiency of an engine at $$T_1=447^{\circ }\mathrm{C}$$ and $${\mathrm{T}}_2=147^{\circ }\mathrm{C}$$ while $${\eta }_2$$ is the efficiency at $${\mathrm{T}}_1=947^{\circ }\mathrm{C}$$ and $${\mathrm{T}}_2=47^{\circ }\mathrm{C}$$ The ratio $$\frac{{\eta }_1}{{\eta }_2}$$ will be :

7 mol of a certain monoatomic ideal gas undergoes a temperature increase of $$40\mathrm{K}$$ at constant pressure. The increase in the internal energy of the gas in this process is : (Given $$\mathrm{R}=8.3{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$$ )

A monoatomic gas at pressure $$\mathrm{P}$$ and volume $$\mathrm{V}$$ is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :

An ice cube of dimensions $$60\mathrm{cm}\times 50\mathrm{cm}\times 20\mathrm{cm}$$ is placed in an insulation box of wall thickness $$1\mathrm{cm}$$. The box keeping the ice cube at $$0^{\circ }\mathrm{C}$$ of temperature is brought to a room of temperature $$40^{\circ }\mathrm{C}$$. The rate of melting of ice is approximately : (Latent heat of fusion of ice is $$3.4\times 10^5\mathrm{J}{\mathrm{kg}}^{-1}$$ and thermal conducting of insulation wall is $$0.05{\mathrm{Wm}}^{-1\circ }{\mathrm{C}}^{-1}$$ )

A gas has $$n$$ degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be :

If $$K_1$$ and $$K_2$$ are the thermal conductivities, $$L_1$$ and $$L_2$$ are the lengths and $$A_1$$ and $$A_2$$ are the cross sectional areas of steel and copper rods respectively such that $$\frac{K_2}{K_1}=9,\frac{A_1}{A_2}=2,\frac{L_1}{L_2}=2$$. Then, for the arrangement as shown in the figure, the value of temperature $$\mathrm{T}$$ of the steel - copper junction in the steady state will be:

Read the following statements : A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice. B. Two bodies $$P$$ and $$Q$$ having equal surface areas are maintained at temperature $$10^{\circ }\mathrm{C}$$ and $$20^{\circ }\mathrm{C}$$. The thermal radiation emitted in a given time by $$\mathrm{P}$$ and $$\mathrm{Q}$$ are in the ratio $$1:1.15$$. C. A Carnot Engine working between $$100\mathrm{K}$$ and $$400\mathrm{K}$$ has an efficiency of $$75\%$$. D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below :

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $$1:4$$, then A. The r.m.s. velocity of gas molecules in two vessels will be the same. B. The ratio of pressure in these vessels will be $$1:4$$. C. The ratio of pressure will be $$1:1$$. D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of $$1:4$$. Choose the correct answer from the options given below :

In $$1^{\text{st }}$$ case, Carnot engine operates between temperatures $$300\mathrm{K}$$ and $$100\mathrm{K}$$. In $$2^{\text{nd }}$$ case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in $$2^{\text{nd }}$$ case) will be :

Which statements are correct about degrees of freedom ? (A) A molecule with n degrees of freedom has n$${}^2$$ different ways of storing energy. (B) Each degree of freedom is associated with $$\frac{1}{2}$$ RT average energy per mole. (C) A monatomic gas molecule has 1 rotational degree of freedom where as diatomic molecule has 2 rotational degrees of freedom. (D) $${\mathrm{CH}}_4$$ has a total of 6 degrees of freedom. Choose the correct answer from the options given below :

A Carnot engine has efficiency of $$50\%$$. If the temperature of sink is reduced by $$40^{\circ }\mathrm{C}$$, its efficiency increases by $$30\%$$. The temperature of the source will be:

Given below are two statements : Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature. Statement II : The rms speed of oxygen molecules in a gas is $$v$$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $$2v$$. In the light of the above statements, choose the correct answer from the options given below :

A vessel contains $$14\mathrm{g}$$ of nitrogen gas at a temperature of $$27^{\circ }\mathrm{C}$$. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be : Take $$\mathrm{R}=8.32\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{k}}^{-1}$$.

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

The root mean square speed of smoke particles of mass $$5\times 10^{-17}\mathrm{kg}$$ in their Brownian motion in air at NTP is approximately. [Given $$\mathrm{k}=1.38\times 10^{-23}{\mathrm{JK}}^{-1}$$]

A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 $$\times$$ 105 NC$$-$$1. If the charge on the particle is 40 $$\mu$$C and the initial velocity is 200 ms$$-$$1, how much distance it will travel before coming to the rest momentarily :

Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulomb's force is :