Embibe Experts Solutions for Chapter: Kinetic Theory of Gases and Thermodynamics, Exercise 1: Exercise 1

A non-conducting container is divided into two chambers that are separated by a valve. The left chamber contains one mole of a monatomic ideal gas. The right chamber is evacuated. At some instant, the valve is opened and the gas rushes freely into the right chamber. Which are of the following statements concerning this process is true?

An ideal gas with adiabatic exponent $\left(\gamma =1.5\right)$ undergoes a process in which work done by the gas is same as increase in internal energy of the gas. The molar heat capacity of gas for the process is 

The ratio of specific heats at constant pressure and constant volume of a gas is $\frac{4}{3}$. Then the average number of degree of freedom of the gas molecules is 

A wall is made of two layers $A$ and $B$ of the same thickness but different materials as shown. The thermal conductivity of $A$ is thrice that of $B$. In steady state, the temperature difference across the wall is $36°\mathrm{C}$. The temperature difference across the layer $A$ is

A rod of length $\ell$ and cross section area $A$ has a variable thermal conductivity given by $k=\alpha T$, where $\alpha$ is positive constant and $T$ is temperature in kelvin. Two ends of the rod are maintained at temperatures $T_1$ and $T_2\left( T_1>T_2\right)$. Heat current flowing through the rod will be

Two identical long, solid cylinders are used to conduct heat from temp $T$, to temp $T_2$. Originally th cylinder are connected in series and the rate of heat transfer is $H$. If the cylinders are connected parallel then the rate of heat transfer would be 

A solid spherical black body of radius $r$ and uniform mass distribution is in free space. It emits power $P$ and its rate of cooling is $R$ then

Two bodies $A$ and $B$ have emissivities $0.5\text{ and} 0.8$, respectively. At some temperatures the two bodies have maximum spectral emissive powers at wavelength $8000 \stackrel{\mathrm{o}}{\mathrm{A}}$ and $4000 \stackrel{\mathrm{o}}{\mathrm{A}}$, respectively. The ratio of their emissive powers at these temperatures is