A spherical shell is heated. The Volume changes according to the equation `V_theta= V_0(1+gamma_theta)`. Does the volume refer to the volume encloded by the shell or the volume of the marerial making up the shell?

An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation p=kv . Show that the molar heat capacity of the gas for the process is given by (C=C_v + ( R)/(2)) .

An egg of a particular bird is very nearly spherical. If the radius to the inside of the shell is 5mm and radius to the outside of the shell is 5.3 mm, find the volume of the shell approximately.

The outer and the inner surface areas of a spherical copper shell are 576 pi cm^(2) and 324 pi cm^(2) respectively. Find the volume of the material required to make the shell.

A cylindrica container is to be made from certain solid material with the following constraints: It has a fixed inner volume of V mm^3 , has a 2 mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness 2mm and is of radius equal to the outer radius of the container. If the volume the material used to make the container is minimum when the inner radius of the container is 10 mm . then the value of V/(250 pi) is

Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.

Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 2%.

Two vessels A and B of equal volume (V_0) are connected by a narrow tube which can be closed by a value. The vessels are fitted with piston which can be moved to change the volumes. Initially, the valve is open and the vessels contain an ideal gas (C_p / C_v = gamma ) at atomspheric pressures (P_0) and atmoshpeheric temperature (T_0) . The walls of the vessels A are diathermic and those of B are adiabatic. The value is now closed and the pistons are slowly pulled out to increase the volumes of the of the vessels to dobuled the original value.(a) Find the temperatures and pressures in the two vessels. (b) The value is now opened for sufficeint time so that the gases acquire a common tempertures and pressures . Find the new values of the temperatuere and the pressures.

Two samples A and B of the same gas have equal volumes and pressures . The gas is sample A is expanded isothermally to double its volume and the the gas in B is expanded adibatically to double its volume . If the work done by the gas is the same for the two cases, show that gamma satisfies the equation (1-2 ^(1-gamma)= (gamma - 1 ) 1n2 .