Acubical container of side a and wall thickness x (a: « a) is suspendedin air and filled n molesof diatomic gas (adiabatic exponent=y) inaroom where room temperature isT^. Ifat/ = 0 gastemperature is Fj (F, > Fq), find the gas temperature as a function of time t. Assume the heat is conducted through all the walls ofcontainer.

A heat-conducting piston can freely move inside a closed thermally insulated cylinder with an ideal gas. In equilibrium the piston divides the cylinder into two equal parts, the gas temperature being equal to T_0 . The piston is slowly displaced. Find the gas temperature as a function of the ratio eta of the volumes of the greater and smaller sections. The adiabatic exponent of the gas is equal to gamma .

An adiabatic cylinder of cross section A is fitted with a mass less conducting piston of thickness d and thermal conductivity K. Initially, a monatomic gas at temperature T_(0) and pressure P_(0) occupies a volume V_(0) in the cylinder. The atmospheric pressure is P_(0) and the atmospheric temperature is T_(1) (gt T_(0)) . Find (a) the temperature of the gas as a function of time (b) the height raised by the piston as a function of time. Neglect friction and heat capacities of the container and the piston.

A monatomic ideal gas is contained in a rigid container of volume V with walls of total inner surface area A, thickness x and thermal conductivity K. The gas is at an initial temperature t_(0) and pressure P_(0) . Find the pressure of the gas as a function of time if the temperature of the surrounding air is T_(s) . All temperature are in absolute scale.

A monatomic ideal gas is contained in a rigid container of volume V with walls of total inner surface area A, thickness x and thermal conductivity K. The gas is at an initial temperature t_(0) and pressure P_(0) . Find the pressure of the gas as a function of time if the temperature of the surrounding air is T_(s) . All temperature are in absolute scale.

(i) A conducting piston divides a closed thermally insulated cylinder into two equal parts. The piston can slide inside the cylinder without friction. The two parts of the cylinder contain equal number of moles of an ideal gas at temperature T_(0) . An external agent slowly moves the piston so as to increase the volume of one part and decrease that of the other. Write the gas temperature as a function of ratio (beta) of the volumes of the larger and the smaller parts. The adiabatic exponent of the gas is gamma . (ii) In a closed container of volume V there is a mixture of oxygen and helium gases. The total mass of gas in the container is m gram. When Q amount of heat is added to the gas mixture its temperature rises by Delta T . Calculate change in pressure of the gas.

A spherical container made of non conducting wall has a small orifice in it. Initially air is filled in it at atmospheric pressure (P_(0)) and atmospheric temperature (T_(0)) . Using a small heater, heat is slowly supplied to the air inside the container at a constant rate of H J/s. Assuming air to be an ideal diatomic gas find its temperature as a function of time inside the container.

monatomic ideal gas is contained in a rigid container of volume V with walls of totsl inner surface area A, thickness x and thermal condctivity K. The gas is at an initial temperature t_(0) and pressure P_(0) . Find tjr pressure of the gas as a function of time if the temperature of the surrounding air is T_(s) . All temperature are in absolute scale.

An ideal gas of molar mass M is enclosed in a vessel of volume of V whose thin walls are kept at a constant temperature T . At a moment t = 0 a small hole of area S is opened, and the gas starts escaping into vacuum. Find the gas concentration n as a function of time t if at the initial moment n (0) = n_0 .