Related InterviewSolutions

• Calculate the value of `gamma` for a gaseous mixture consisting `n_(1)` moles of oxygen and `n_(2)` moles of carbon dioxide. The values of `gamma` for oxygen and carbon dioxide are `gamma_(1)` and `gamma_(2)` respectively. Assume the gases to be ideal.
• One mole of a gas is in state `A[P, V, T_(A)]`. A small adiabatic process causes the state of the gas to change to `B [P + dP, V + dV, T_(B)]`. The changes dV & dP are infinitesimally small and dV is negative. An alternative process takes the gas from state A to B via `A rarr C rarr B`. `A rarr C` is isochoric and `C rarr B` is isobaric path. State at C is `[P + dP, V, T_(C)]`. (a) Rank the temperatures `T_(A), T_(B)` and `T_(C)` from highest to lowest. (b) Find g of the gas in terms of `T_(A)`, `T_(B)` and `T_(C)`.
• A bullet of lead melts when stopped by obstacle. Assuming that 25 per cent of the heat is absorbed by the osbtacle, find the velocity of the bullet if its initial temperature is `27^(@)C`. (Melting point of lead `327^(@)C`, specific heat capacity of lead `=30 cal kg^(-1)K^(-1)` specific latent heat of fusion of lead `=6000 cal kg^(-1)` and `J=4.2` joules `cal^(-1)`)
• Calculate the amount of heat required in calorie to change 1 g of ice at `-10^(@)C` to steam at `120^(@)C`. The entire process is carried out at atmospheric pressure. Specific heat of ice and water are `0.5 cal g^(-1) .^(@)C^(-1)` and `1.0 cal g^(-1) .^(@)C^(-1)` respectively. Latent heat of fusion of ice and vaporization of water are `80 cal g^(-1)` and `540 cal g^(-1)` respectively. Assume steam to be an ideal gas with its molecules having 6 degrees of freedom. Gas constant `R = 2 cal mol^(-1) K^(-1)`.
• A gas-gun has a cylindrical bore made in an insulating material. Length of the bore is L. A small bullet having mass m just fits inside the bore and can move frictionlessly inside it. Initially n moles of helium gas is filled in the bore to a length `L_(0)`. The bullet does not allow the gas to leak and the bullet itself is kept at rest by a stopper S. The gas is at temperature `T_(0)`. The gun fires if the stopper S is removed suddenly. Neglect atmospheric pressure in your calculations [Think that the gun is in space]. (a) Calculate the speed with which the bullet is ejected from the gun. (b) Find the maximum possible speed that can be imparted to the bullet by using n moles of helium at temperature `T_(0)`.
• 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.
• A tube of length `2m` containing a little mercury and closed at both ends is rapidly inverted 50 times. What is the maximum rise in temperature expected? (Specific heat capacity of mercury `=30calkg^(-1) K^(-1)` and `J=4.2` joules//cal.)
• Air is filled inside a jar which has a pressure gauge connected to it. The temperature of the air inside the jar is same as outside temperature `(= T_(0))` but pressure `(P_(1))` is slightly larger than the atmospheric pressure `(P_(0))`. The stopcock is quickly opened and quickly closed, so that the pressure inside the jar becomes equal to the atmospheric pressure `P_(0)`. The jar is now allowed to slowly warm up to its original temperature `T_(0)`. At this time the pressure of the air inside is `P_(2) (P_(0) lt P_(2) lt P_(1))`. Assume air to be an ideal gas. Calculate the ratio of specific heats `(= gamma)` for the air, in terms of `P_(0), P_(1)` and `P_(2)`.
• A sample of oxygen is heated in a process for which the molar specific heat capacity is 2R. During the process the temperature becomes `(32)^(1//3)` times of the original temperature. How does the volume of the gas change?
• An ideal diatomic gas undergoes a process in which the pressure is proportional to the volume. Calculate the molar specific heat capacity of the gas for the process.