$A$ monoatomic gas of $n$-moles is heated from temperature $T_1$ to $T_2$ under two different conditions: $(i)$ at constant volume and (ii) at constant pressure. The change in internal energy of the gas is

An ideal monoatomic gas expands to twice its volume. If the process is isothermal,the magnitude of work done by the gas is $W_i$. If the process is adiabatic,the magnitude of work done by the gas is $W_a$. Which of the following is true?

For an ideal gas,which of the following statements is correct?

In Column $-I$ processes and in Column $-II$ formulas of work are given. Match them appropriately:

Column $-I$	Column $-II$
$(a)$ Isothermal process	$(i)$ $W = \frac{\mu R(T_1 - T_2)}{\gamma - 1}$
$(b)$ Adiabatic process	$(ii)$ $W = P\Delta V$
	$(iii)$ $W = 2.303\mu RT \log_{10} \left( \frac{V_2}{V_1} \right)$

Two samples $A$ and $B$ of a gas,initially at the same pressure and temperature,are compressed from volume $V$ to $V/2$. Sample $A$ is compressed isothermally,and sample $B$ is compressed adiabatically. The final pressure of $A$ is:

One mole of a monoatomic ideal gas goes through a thermodynamic cycle,as shown in the volume versus temperature $(V-T)$ diagram. The correct statement$(s)$ is/are :
[$R$ is the gas constant]
$(1)$ Work done in this thermodynamic cycle $(1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 1)$ is $|W| = \frac{1}{2} RT_0$
$(2)$ The ratio of heat transfer during processes $1 \rightarrow 2$ and $2 \rightarrow 3$ is $\left|\frac{Q_{1 \rightarrow 2}}{Q_{2 \rightarrow 3}}\right| = \frac{5}{3}$
$(3)$ The above thermodynamic cycle exhibits only isochoric and adiabatic processes.
$(4)$ The ratio of heat transfer during processes $1 \rightarrow 2$ and $3 \rightarrow 4$ is $\left|\frac{Q_{1 \rightarrow 2}}{Q_{3 \rightarrow 4}}\right| = \frac{1}{2}$