First Law of Thermodynamics

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loading piston (as shown in Fig $20.63$). Initially the gas is at temperature $T_1$ pressure $P_1$ and volume $V_1$ and the spring is in relaxed state. The gas is then Fig. $20.63$ heated very slowly to temperature $T_2$, pressure $p_2$ and volume $V_2$. During this process the piston moves out by a distance $X$. Ignoring the friction between the piston and the cylinder, the correct statements $\left(s\right)$ is (are)

For the following two isotherms drawn at two different temperature ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ which of the following statement is true? ( number of moles are constant )

An ideal gas at $27°\mathrm{C}$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. The rise in temperature is (Take $\mathrm{\gamma } =\frac{5}{3}$)

Show that slope of adiabatic curve is $\mathrm{\gamma }$ times the slope of isothermal process.

The slope of isothermal and adiabatic curves are related as

The graph for Boyle's law is called

An ideal gas is allowed to expand freely against vacuum in a rigid insulated container. The gas undergoes

An ideal is filled in a closed, rigid and thermally-insulated container. A coil of $100\mathrm{\Omega }$ resistance and carrying a current of $1 \mathrm{A}$ supplies heaT to the gas. The change in the internal energy of the gas after $5$ minutes will be:

During an adiabatic expansion, a gas does $50 \mathrm{J}$ of work against the surroundings. It is then cooled at constant volume by removing $20 \mathrm{J}$ of energy from the gas. The magnitude of the total change in internal energy of the gas is $x \mathrm{J}$. The value of $x$ is

A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is $T{V}^x=$ constant, then $x$ is:

A cycle tyre bursts suddenly. What is the type of this process?

One mole of helium is adiabatically expanded from its initial state $\left(p_i,V_i,T_i\right)$ to its final state $\left(p_f,V_f,T_f\right)$. The decrease in the internal energy associated with this expansion is equal to

A container of volume $1 {\mathrm{m}}^3$ is divided into two equal compartments by a partition. One of these compartments contains an ideal gas at $300 \mathrm{K}$. The other compartment is vacuum. The whole system is thermally isolated from its surroundings. The partition is removed in the gas container. Its temperature now would be

Six moles of an ideal gas performs a cycle shown in the figure. If the temperatures are $T_{\mathrm{A}}=600 \mathrm{K}\text{,} T_{\mathrm{B}}=800 \mathrm{K}$, $T_{\mathrm{C}}=2200 \mathrm{K}$ and $T_{\mathrm{D}}=1200 \mathrm{K},$ then work done per cycle is approximately___ (Take $R=8.3 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$)

Two identical cylinders $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $\mathrm{V}$. The mass of the gas in $A$ is $m_A$ and that in $B$ is $m_B$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2\mathrm{V}$. The change in the pressure in $A$ and $B$ are found to be $∆P$ and $1.5 ∆P$ respectively. Then

P-V plots for two gases during adiabatic processes are shown in the figure. Plots $1$ and $2$ should correspond respectively to:

In adjoining diagram, no heat exchange between the gas and the surroundings will take place if the gas is taken along:

One mole of an ideal gas at pressure $P_0$ and temperature $T_0$ volume $V_0$ is expanded isothermally to twice its volume and then compressed at constant pressure to $\left(V_0/2\right)$ and the gas is brought to its original state by a process in which $P\propto V$ (Pressure is directly proportional to volume). The correct representation of the process is

One mole of an ideal monatomic gas is taken through a semicircular thermodynamic process $ACB$ shown in the $P–V$ diagram. The heat supplied to the system is

One mole of an ideal gas is taken through the process, $ABC$ as shown in the figure. The temperature of the gas at $A$ is $T_0$​.The total work done on the gas is,