First Law of Thermodynamics

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

If the temperature falls then $\Delta U$ is _____.

Work done by the gas or any system is always positive.

When heat is supplied to the system then $\Delta Q$ is ____ and $\Delta Q$ is ____ when heat is extracted from the system. Choose the appropriate option.

$1 \mathrm{mole}$ of rigid diatomic gas performs a work of $\frac{\mathrm{Q}}{5}$ when heat $\mathrm{Q}$ is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{\mathrm{xR}}{8}.$ The value of $\mathrm{x}$ is ________ .

A monatomic ideal gas undergoes a process $ABC$. The heat given to the gas 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

An electric heater supplies heat to a system at a rate of $100 W\mathit{.}$ If the system performs Work at a rate of $60$ joules per second, the rate at which internal energy changes is

$1 \mathrm{gm}$ of water at $100 °\mathrm{C}$, is completely converted to steam at $100 °\mathrm{C}$, occupies $1800 \mathrm{cc}$. The increase in the internal energy of the molecules is:
(take the pressure $={10}^5 \mathrm{Pa}$, Latent heat of vaporisation $\left(L\right)=540 \mathrm{cal} {\mathrm{gm}}^{-1},1\mathrm{cal}=4.2 \mathrm{J}$)

As shown in the figure, the amount of heat absorbed along the path $ABC$ is $90 \mathrm{J}$ and the amount of work done by the system is $30 \mathrm{J}$. If the amount of work done along the path $ADC$ is $20 \mathrm{J}$ the amount of heat absorbed will be:

When a system is taken from state $\mathrm{i}$ to state $\mathrm{f}$ along the path $\mathrm{iaf}$, it is found that $Q\mathit{=}50 \mathrm{cal}$ and $W=20 \mathrm{cal}$. Along the path $\mathrm{ibf}$, $Q=36 \mathrm{cal}$. Work (in $\mathrm{cal}$) along the path $\mathrm{ibf}$ is-

In thermodynamic process pressure of a fixed mass of gas is changed in such a manner that the gas releases $30$ joule of heat and $18$ joule of work was done on the gas. If the initial internal energy of the gas was $60$ joule, then, the final internal energy (in J) will be:

A thermodynamic process is shown in the figure. The pressures and volumes corresponding to some points in the figure are: $P_{\mathrm{A}}=3\times {10}^4 \mathrm{Pa}\text{,} P_{\mathrm{B}}=8\times {10}^4 \mathrm{Pa}$ and $V_{\mathrm{A}}=2\times {10}^{-3} {\mathrm{m}}^3\text{,} V_{\mathrm{D}}=5\times {10}^{-3} {\mathrm{m}}^3$. In process $AB\text{,} 600 \mathrm{J}$ of heat is added to the system and in process $BC\text{,} 200 \mathrm{J}$ of heat is added to the system. The change in internal energy(in $\mathrm{J}$) of the system in the process $AC$ would be,

In a cyclic process, change in internal energy is zero.

A closed vessel $10 \mathrm{L}$ in volume, contains a diatomic gas under a pressure of ${10}^5 \mathrm{N} {\mathrm{m}}^{-2}$. What amount of heat should be imparted to the gas to increase the pressure in the vessel by five times?

Two moles of helium gas undergo a cyclic process as shown. Assuming the gas to be ideal, the difference in heat absorbed and heat rejected by the gas is $xR\ln \left(2\right)$. Write the value of $x$.

The molar heat capacity for the process is $xR$ , where $R$  is gas constant, when $10 \mathrm{J}$ of heat added to a monoatomic ideal gas, then gas performs a work of $5 \mathrm{J}$ on its surrounding, then $x$ is.

Which one of the following is not true in a thermodynamic process?

A cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in figure. The heat exchanged by the engine with the surroundings at constant volume is: ($\mathrm{ }{C}_{\mathit{V}}=\frac{3}{2}R$, $P_A$ and $P_B$ are the pressures of the gas at point $A$ and point $B$ respectively, and $V_A$ is the volume of the gas at point $A$)

When the state of a gas adiabatically changed from an equilibrium state $A$ to another equilibrium state $B,$ an amount of work done on the system is $35 \mathrm{J}$. If the gas is taken from state $A$ to $B$ via a process in which the net heat absorbed by the system is $12 \mathrm{Cal}$, the word done by the substance will be