D. C. Pandey Solutions for Chapter: The First Law of Thermodynamics, Exercise 2: Excercise 2

In a process, temperature and volume of one mole of an ideal mono-atomic gas are varied according to the relation, $VT=k$, where $k$ is a constant. In this process, the temperature of the gas is increased by $\Delta T$. The amount of heat absorbed by gas is (where $R$ is gas constant),

The given diagram shows four processes, i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes in the same order is given by,

An ideal mono-atomic gas at $300 \mathrm{K}$ expands adiabatically to twice its volume. The final temperature of gas is,

One mole of Nitrogen gas being initially at a temperature, $T_0=300 \mathrm{K}$ is adiabatically compressed to increase its pressure $10$ times. The final gas temperature after compression is (assume Nitrogen gas molecules as rigid and diatomic and ${100}^{\frac{1}{7}}=1.9$),

If the speed of sound in a mixture of $2$ moles of Helium and $2$ moles of Hydrogen at temperature $\frac{972}{5} \mathrm{K}$ is $n\times 100 \mathrm{m} {\mathrm{s}}^{-1}$, then the value of $n$ is (Take, $R=\frac{25}{2} \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$)

One mole of a monatomic ideal gas undergoes the process $A\to B$ in the given $p-V$ diagram. Specific heat capacity in the process is

If $\alpha$ is the coefficient of performance of a refrigerator and $Q_1$ is heat released to the hot reservoir, then the heat extracted from the cold reservoir $Q_2$ is,

Consider the given diagram. An ideal gas is contained in a chamber (left) of volume $V$ and is at an absolute temperature $T$. It is allowed to rush freely into the right chamber of volume $V$ which is initially vacuum. The whole system is thermally isolated. What will be the final temperature of the equilibrium has been attained?