Internal Energy and Work Done in Thermodynamics

A non-conducting cylindrical vessel of length, $3l$ is placed horizontally & is divided into three parts by two easily moving pistons having low thermal conductivity as shown in the figure. These parts contains ${\mathrm{H}}_2, \mathrm{He}$ and ${\mathrm{CO}}_2$ gad at initial temp. ${\theta }_1={372}^0\mathrm{C}$, ${\theta }_2={15}^0\mathrm{C}$ and ${\theta }_3={157}^0\mathrm{C}$ respectively. If the initial length and pressure of each part are $l$ and $P_0$ respectively, calculate the final pressure and length of each part. Use: ${\gamma }_{{\mathrm{co}}_2}=\frac{7}{5}$.

The pressure in monoatomic gas increases linearly from $4\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$ to $8\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$ when its volume increases from $0.2 {\mathrm{m}}^3$ to $0.5 {\mathrm{m}}^3$.

(i) If work done by the gas is $1.8\times {10}^{\mathrm{y}} \mathrm{J}$ then find the value of $y$.

(ii) If increase in internal energy is $1.6z\times {10}^5 \mathrm{J}$ then find the value of $z$.

(iii) If amount of heat supplied is $6.6\times {10}^{\mathrm{x}} \mathrm{J}$ then find the value of $x$.

(iv) If molar specific heat of the gas is $1.71\times {10}^{\mathrm{\alpha }} \mathrm{J} \mathrm{mole}-{\mathrm{K}}^{-1}$ then find the value of $\alpha$.

One mole of monoatomic ideal gas undergoes a cyclic process $\mathrm{ACBA}$ as shown in figure. Process $\mathrm{AC}$ is adiabatic. The temperatures at $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are $300 \mathrm{K}, 600 \mathrm{K}$ and $450 \mathrm{K}$ respectively:-

One mole of an ideal monatomic gas is taken from $\mathrm{A}$ to $C$ along the path $ABC.$ The temperature of the gas at $A$ is $T_0.$ For the process $ABC$

A thermally insulated chamber of volume $2V_0$ is divided by a frictionless piston of area $S$ into two equal parts $\mathrm{A}$ and $\mathrm{B}$. Part $\mathrm{A}$ has an ideal gas at pressure $P_0$ and temperature $T_0$ and in part $\mathrm{B}$ is vacuum. A massless spring of force constant $k$ is connected with piston and the wall of the container as shown. Initially spring is unstarched. Gas in chamber $\mathrm{A}$ is allowed to expand. Let in equilibrium spring is compressed by $x_0$ . Then

An ideal monatomic gas undergoes a cyclic process $\mathrm{ABCA}$ as shown in the figure. The ratio of heat absorbed during $\mathrm{AB}$ to the work done on the gas during $\mathrm{BC}$ is:

An ideal gas is heated from temperature $T_1$ to $T_2$ under various conditions. The correct statement(s) is/are:-