Physics Test 171

4 gms of steam at 100°C is added to 20 gms of water at 46°C in a container of negligible mass. Assuming no heat is lost to surrounding, the mass of water in container at thermal equilibrium is. Latent heat of vaporisation = 540 cal/gm. Specific heat of water = 1 cal/gm-°C.

A diatomic ideal gas undergoes a thermodynamic change according to the P–V diagram shown in the figure. The total heat given to the gas is nearly (use ln₂ = 0.7) :

Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be (α₁, α₂ = linear expansion co-efficient A₁, A₂ = Area of rods Y₁, Y₂ = Young modulus)

For a gas sample with N₀ number of molecules, function N(V) is given by : 

Where dN is number of molecules in speed range V to V+ dV. The rms speed of the molecules is :

The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula α = a T, where a is a positive constant and T in ºC. If the length of the rod is l at temperature 0 ºC, then the temperature at which the length will be 2 l is:

A black body emits radiation at the rate P when its temperature is T. At this temperature the wavelength at which the radiation has maximum intensity is λ₀. If at another temperature T' the power radiated is P' and wavelength at maximum intensity is  then

Thermal coefficient of volume expansion at constant pressure for an ideal gas sample of n moles having pressure P₀, volume V₀ and temperature T₀ is

There are two thin spheres A and B of the same material and same thickness. They emit like black bodies. Radius of A is double that of B. A and B have same temperature T. When A and B are kept in a room of temperature T0 (< T), the ratio of their rates of cooling (rate of fall of temperature) is: [assume negligible heat exchange between A and B]

A piston can freely move inside a horizontal cylinder closed from both ends. Initially, the piston separates the inside space of the cylinder into two equal parts each of  volume V₀ , in which an ideal gas is contained under the same pressure p₀ and at the same temperature. What work has to be performed  in order to increase isothermally the volume of one part of gas 2 times compared to that of the other by slowly moving the piston ?

A uniform pressure P is exerted by an external agent on all sides of a solid cube at temperature tºC. By what amount should the temperature of the cube be raised in order to bring its volume back to its original volume before the pressure was applied if the bulk modulus is B and co-efficient of volumetric expansion is γ ?