Thermodynamics PYQ — Page 10

At what temperature a gold ring of diameter $6.230\mathrm{cm}$ be heated so that it can be fitted on a wooden bangle of diameter $6.241\mathrm{cm}$? Both the diameters have been measured at room temperature $(27^{\circ}C)$. (Given: coefficient of linear thermal expansion of gold ${\alpha }_{L}=1.4\times {10}^{-5}{K}^{-1}$)

The relation between root mean square speed $({v}_{\mathrm{rms}})$ and most probable speed $({v}_{p})$ for the molar mass $M$ of oxygen gas molecule at the temperature of $300K$ will be

According to kinetic theory of gases, A. The motion of the gas molecules freezes at $0^{\circ}C$. B. The mean free path of gas molecules decreases if the density of molecules is increased. C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant. D. Average kinetic energy per molecule per degree of freedom is $\frac{3}{2}{k}_{B}T$ (for monoatomic gases). Choose the most appropriate answer from the options given below

An ideal gas undergoes a cyclic process ABCA where AB is isothermal...

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

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 

Two metallic wires of identical dimensions are connected is series. If ${\sigma }_{1}$ and ${\sigma }_{2}$ are the conductivities of the these wires respectively, the effective conductivity of the combination is :

A $100g$ of iron nail is hit by a $1.5\mathrm{kg}$ hammer striking at a velocity of $60{\mathrm{ms}}^{-1}$. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail ? [Specific heat capacity of iron $=0.42{\mathrm{Jg}}^{-1}{C\circ }^{-1}$]

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 monoatomic 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 to $6$ degrees of freedom. Choose the correct answer from the option given below:

A sample of an ideal gas is taken through the cyclic process $ABCA$ as shown in figure. It absorbs, $40J$ of heat during the part $AB$, no heat during $BC$ and rejects $60J$ of heat during $CA$. A work of $50J$ is done on the gas during the part $BC$. The internal energy of the gas at $A$ is $1560J$. The work done by the gas during the part $CA$ is 

Nearly $10%$ of the power of a $110W$ light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of $1m$ from the bulb to a distance of $5m$ is $a\times {10}^{-2}W{m}^{-2}$. The value of '$a$' will be

Following statements are given (1) The average kinetic energy of a gas molecule decreases when the temperature is reduced. (2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature. (3) The average kinetic energy of a gas molecule decreases with increases in volume. (4) Pressure of a gas increases with increase in temperature at constant volume. (5) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below :

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

A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $1.4$. Vessel is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by : ($R=$ universal gas constant)

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

A steam engine intakes $50g$ of steam at $100^{\circ}C$ per minute and cools it down to $20^{\circ}C$. If latent heat of vaporization of steam is $540\mathrm{cal}{g}^{-1}$, then the heat rejected by the steam engine per minute is _____ $\times {10}^{3}\mathrm{cal}$ (Given : specific heat capacity of water : $1\mathrm{cal}{g}^{-1}{C\circ }^{-1}$)

A diatomic gas $(\gamma =1.4)$ does $400J$ of work when it is expanded isobarically. The heat given to the gas in the process is _____ $J$.

A cylindrical container of volume $4.0\times {10}^{-3}{m}^{3}$ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is $400K$. The pressure of the mixture of gases is : [Take gas constant as $8.3J{\mathrm{mol}}^{-1}{K}^{-1}]$

Which one is the correct option for the two different thermodynamic processes ? 

In a certain thermodynamical process, the pressure of a gas depends on its volume as $k{V}^{3}$. The work done when the temperature changes from $100^{\circ}C$ to $300^{\circ}C$ will be $xnR$ where $n$ denotes number of moles of a gas find $x$ ;

A sample of gas with $\gamma =1.5$ is taken through an adiabatic process in which the volume is compressed from $1200{\mathrm{cm}}^{3}$ to $300{\mathrm{cm}}^{3}.$ If the initial pressure is $200\mathrm{kPa}.$ The absolute value of the workdone by the gas in the process $=________J.$

A monoatomic ideal gas, initially at temperature ${T}_{1}$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature ${T}_{2}$ by releasing the piston suddenly. If ${l}_{1}$ and ${l}_{2}$ are the lengths of the gas column, before and after the expansion respectively, then the value of $\frac{{T}_{1}}{{T}_{2}}$ will be:

The volume $V$ of an enclosure contains a mixture of three gases, $16g$ of oxygen, $28g$ of nitrogen and $44g$ of carbon dioxide at absolute temperature $T$. Consider $R$ as universal gas constant. The pressure of the mixture of gases is :

A mixture of hydrogen and oxygen has volume $500{\mathrm{cm}}^{3},$ temperature $300K,$ pressure $400k\mathrm{Pa}$ and mass $0.76g.$ The ratio of masses of oxygen to hydrogen will be: