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Thermal Properties Of Matter

Q: 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

Let there are n_{1} moles of hydrogen and n_{2} moles of helium in the given mixture. As Pv = nRT Then the pressure of the mixture P = \dfrac {n_{1}RT}{V} + \dfrac {n_{2}RT}{V} = (n_{1} + n_{2}) \dfrac {RT}{V} \Rightarrow 2\times 101.3\times 10^{3} = (n_{1} + n_{2}) \times \dfrac {(8.3\times 300)}{20\times 10^{-3}} or, (n_{1} + n_{2}) = \dfrac {2\times 101.30 \times 10^{3} \times 20\times 10^{-3}}{(8.3)(300)} or, n_{1} + n_{2} = 1.62 .... (1) The mass of the mixture is (in grams) n_{1}\times 2 + n_{2} \times 4 = 5 \Rightarrow (n_{1} + 2n_{2}) = 2.5 ..... (2) Solving the eqns. (1) and (2) , we get n_{1} = 0.74 and n_{2} = 0.88 Hence, \dfrac {m_{H}}{m_{He}} = \dfrac {0.74\times 2}{0.88\times 4} = \dfrac {1.48}{3.52} = \dfrac {2}{5} .

Q: 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?

Heat flow through vacuum is possible in radiation mode due to which temperature of hot body falls.

Q: 0.5 moles of an ideal gas at constant temperature 27^{\circ}C kept inside a cylinder of length L and cross-section area A closed by a massless piston.The cylinder is attached with a conducting rod of length L , cross-section area (\dfrac{1}{9})m^{2} and thermal conductivity k , whose other end is maintained at 0^{\circ}C . If piston is moved such that rate of heat flow through the conducing rod is constant then velocity of piston when it is at height \dfrac{L}{2} from the bottom of cylinder is:[Neglect any kind of heat loss from system]

\dfrac {\triangle Q}{\triangle t} = \dfrac {\triangle W}{\triangle t} = work done per unit time = \dfrac {ka\theta}{L} \dfrac {dW}{dt} = P \dfrac {dv}{dt} = k \dfrac {a\theta}{L}, P = \dfrac {nRT}{V} \Rightarrow \dfrac {0.5R(300}{V} A. \dfrac {dl}{dt} = \dfrac {ka\theta}{L} \Rightarrow \dfrac {0.5R(300)}{A.\dfrac {L}{2}}A.v = \dfrac {ka\theta}{L} \Rightarrow v = \dfrac {ka}{R}\left (\dfrac {27}{300}\right ) = \dfrac {k}{100R} .

Physics
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JEE Mains JEE Advanced NEET BITSAT Easy Qs Med Qs Hard Qs

A vessel of volume $20 L$ contains a mixture of hydrogen and helium at temperature of $2 7^{\circ} C$ and pressure $2 a t m$ . 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

1 : 2

2 : 3

2 : 1

2 : 5

Hard

BITSAT

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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?

Radiation

Convection

Conduction

Temperature remains unchanged

Easy

BITSAT

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$0.5$ moles of an ideal gas at constant temperature $2 7^{\circ} C$ kept inside a cylinder of length $L$ and cross-section area $A$ closed by a massless piston.
The cylinder is attached with a conducting rod of length $L$ , cross-section area $(\frac{1}{9}) m^{2}$ and thermal conductivity $k$ , whose other end is maintained at $0^{\circ} C$ . If piston is moved such that rate of heat flow through the conducing rod is constant then velocity of piston when it is at height $\frac{L}{2}$ from the bottom of cylinder is:
[Neglect any kind of heat loss from system]

(\frac{k}{R}) m / s e c

(\frac{k}{1 0 R}) m / s e c

(\frac{k}{1 0 0 R}) m / s e c

(\frac{k}{1 0 0 0 R}) m / s e c

Hard

BITSAT

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Thermal Properties Of Matter

Physics 244 Views

A vessel of volume 20 L contains a mixture of hydrogen and helium at temperature of 27∘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?

Physics
244 Views

A vessel of volume $20 L$ contains a mixture of hydrogen and helium at temperature of $2 7^{\circ} C$ and pressure $2 a t m$ . 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