Thermal Propert...

Three perfect gases at absolute temperatures $$\mathrm{T}_{1},\ \mathrm{T}_{2}$$ and $$\mathrm{T}_{3}$$ are mixed. The masses of molecules are $$\mathrm{m}_{1},\ \mathrm{m}_{2}$$ and $$\mathrm{m}_{3}$$ and the number of molecules are $$\mathrm{n}_{1},\ \mathrm{n}_{2}$$ and $$\mathrm{n}_{3}$$ respectively. Assuming no loss of energy, the final temperature of the mixture is:

An ideal gas goes through a reversible cycle $$a\rightarrow b\rightarrow c\rightarrow d$$ has the V- T diagram shown below. Process $$d\rightarrow a $$ and $$b\rightarrow c$$ are adiabatic.
The corresponding P-V diagram for the process is ( all figure are schematic and not drawn to scale).

A leak proof cylinder of length $$1m$$, made of a metal which has low coefficient of expansion is floating vertically in water at $$0^oC$$ such that its height above the water surface is $$20cm$$. When the temperature of water is increased to $$4^oC$$, the height of the cylinder above the water surface becomes $$21cm$$. The density of water at $$T = 4^oC$$, relative to the density at $$T = 0^oC$$ is close to:

Which of the following shows the correct relationship between the pressure $$'P'$$ and density $$\rho$$ of an ideal gas at constant temperature ? 

$$100$$ $$\mathrm{g}$$ of water is heated from $$30^{\mathrm{o}}\mathrm{C}$$ to $$50^{\mathrm{o}}\mathrm{C}$$. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is $$4184$$ $$ \mathrm{J}/\mathrm{K}\mathrm{g}/\mathrm{K}$$)  

Two moles of an ideal gas with $$\dfrac{C_P}{C_V}=\dfrac{5}{3}$$ are mixed with $$3$$ moles of another ideal gas with $$\dfrac{C_P}{C_V}=\dfrac{4}{3}$$. The value of $$\dfrac{C_P}{C_V}$$ for the mixture is :

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2:3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4:3. The ratio of their densities is

A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. which of the following gives the density of the gas?

A vessel of volume $$20\ L$$ contains a mixture of hydrogen and helium at temperature of $$27^{\circ}C$$ and pressure $$2\ atm$$. The mass of mixture is $$5\ g$$. Assuming the gases to be ideal, the ratio of mass of hydrogen to that of the helium in the given mixture will be

A hot and a cold body are kept in vacuum separated from each other. Which of the following causes decrease in temperature of the hot body?