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}\$.

Question 1

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?

Accepted Answer

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

Question 2

$0.5$ 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]

Accepted Answer

$\dfrac {\triangle Q}{\triangle t} = \dfrac {\triangle W}{\triangle t} =$ 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}$.

Thermal Properties Of Matter

Physics
3876 Views

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?

Thermal Properties Of Matter

Physics 3876 Views

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
3876 Views