At constant pressure how much fraction of heat supplied to gas is converted into mechanical work ?  

A gas compressed to half of its volume at ${30}^{o}C$. Upto what temperature should it be heated, so that its volume increase to double of its original volume?

An ideal gas is expanding,such that $P T^2= constant$.The coefficient of volume expansion of the gas is 

A gas follows $VT^2 =$ const. Its volume expansion coefficient will be :-

A one litre flask contain some mercury. It is found that at different temperatures the volume of air inside the flask remain same. the volume of mercury taken in the flask is (coefficient of linear expansion of volume expansion of $Hg$ is $1.8\times { 10 }^{ -4 }/ _{  }^{ o }{ C }$ 

A uniform steel rod has length $\ell$ at $0^oC$. Now one of its end is kept in ice $(0^oC)$ and the other end is kept in steam $(100^oC)$. If the coefficient of thermal expansion of the rod is $\alpha,$how much is the thermal expansion of the rod at steady state? 

An inflated rubber balloon contains one mole of an ideal gas. Has a pressure p, volume V and temperature T. if the temperature rises to 1.1 T, and the volume is increase to 1.05 V, the final pressure will be:

The pressures of a gas in the bulb of constant volume gas thermometer at 0$^{0}$ C are 54.6 cm and 74.6cm of Hg respectively. The pressure at 50$^{0}$ C is:

A vessel contains 1 mole of an ideal monoatomic gas. The coefficient of volume expansion of the gas is $\alpha $. 2 moles of a diatmoic; ideal gas is then introduced into the same vessel. The coefficient of the volume expansion of the mixture will be

If at $60^\circ$C and 80 cm of mercury pressure, a definite mass of a gas is compressed slowly, then the final pressure of the gas if the final volume is half of the initial volume $ (\gamma = \dfrac { 3 }{ 2 }$) is:

The coefficient of volume expansion of liquid is $\gamma$. The fractional change in its density for $\triangle T$ rise in temperature is ?

$1$ mole of a gas with $\gamma =\dfrac{7}{5}$ is mixed with $1$ mole of gas with $\gamma =\dfrac{5}{3}$, the value of $\gamma$ of the resulting mixture of.

If $T$ represent the absolute temperature of an ideal gas, the volume coefficient of thermal expansion at constant pressure, is :

A glass capillary tube sealed at both ends is 100cm long. It lies horizontally with the middle 10cm containing mercury. The two ends of the tube which are equal in length contain air at $27 ^ { 0 } \mathrm { C }$ at a pressure of 76cm of Hg. Now the air column at one end of the tube is kept at $0 ^ { 0 } \mathrm { C }$ and the other end is maintained at $127 ^ { \circ } C$. Calculate the pressure of the air column at $0 ^ { \circ } \mathrm { C }$. (Neglect the change in volume of Hg and glass).

One mole of n ideal monatomic  gas undergoes the following four reversible processes:
Step I: It is first compresses adiabatically from volume $V _1$ to $1m^3$.
Step II: then expanded isothermally to volume $10 m^3$.
Step III: then expanded adiabatically to volume $V _3$.
Step IV: then compressed isothermally to volume $V _1$.
If the efficiency of the above cycle is $3/4$ then V, is

Solid floating in a liquid . On decreasing the temperature solid sinks into the liquid . If ${ \Upsilon  } _{ l }\quad and\quad { \alpha  } _{ s }$ are volume expansion coefficient of liquid and linear expansion coefficient of solid , then :

The SI unit for the coefficient of cubical expansion is

Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density $\rho$ remains uniform throughout the volume. The rate of fractional change in density $\left(\dfrac{1}{p}\dfrac{d\rho}{dt}\right)$ is constant. The velocity v of any point on the surface of the expanding sphere is proportional to.