0.5 moles of an ideal gas at constant temperature 27∘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 (19)m2 and thermal conductivity k, whose other end is maintained at 0∘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 L2 from the bottom of cylinder is:
[Neglect any kind of heat loss from system]
△Q△t=△W△t= work done per unit time =kaθL
dWdt=Pdvdt=kaθL,P=nRTV
⇒0.5R(300VA.dldt=kaθL
⇒0.5R(300)A.L2A.v=kaθL
⇒v=kaR(27300)=k100R.
An ideal monatomic gas is confined in a cylinder by a spring - loaded Piston of cross - section 8.0×10−3m2.Initially the gas is at 300 K and occupies a volume of 2.4×10−3m3 and the spring is in its relaxed state. The gas is heated by a small heater until the piston moves slowly by 0.1 m. Calculate the final temperature of the gas. The force constant of the spring is 8000 N/m, and the atmospheric pressure is 1.0×105N/m2. The cylinder and the Piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. Neglect any heat - loss through the lead wires of the heater. The heat capacity of the heater coil is negligible.
A cylinder of cross section area A has two pistons of negligible mass separated by distance l loaded with spring of negligible mass. An ideal gas at temperature T1 is in the cylinder when the springs are relaxed. When the gas is heated by some means, its temperature becomes T2 and the springs get compressed by l/2 each. If P0 is atmospheric pressure and spring constant k=2P0Al, then the ratio of T2 and T1 is
Seven rods A, B, C, D, E, F and G are joined as shown in figure (28-E9). All the rods have equal cross-sectional area A and length l. The thermal conductivities of the rods are KA = KC = K0, KB = KD = 2K0, KE = 3K0, KF = 4K0 and KG = 5K0. The rod E is kept at a constant temperature T1 and the rod G is kept at a constant temperature T2 (T2 > T1). (a) Show that the rod F has a uniform temperature T = (T1 + 2T2)/3. (b) Find the rate of heat flowing from the source which maintains the temperature T2.
