First Law of Thermodynamics

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

If an ideal diatomic gas follows the process as shown in graph, where $T$ is temperature in $\mathrm{kelvin}$ and $V$ is volume in ${\mathrm{m}}^3$, then molar heat capacity for this process will be [in terms of gas constant $R$],

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

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

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 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 a mono-atomic gas undergoes the processes $1-2$ and $2-3$ as shown. The corresponding graph for the above process for $2$ moles of the gas is

A given mass of gas at a pressure $P$ and absolute temperature $T$ obeys the law $P\propto T^3$ during an adiabatic process. The adiabatic bulk modulus of the gas at a pressure $P$ is

The workdone on the system in changing the state of a gas adiabatically from equilibrium state $A$ to equilibrium state $B$ is $32.4 \mathrm{J}$. If the gas is taken from state $A$ to $B$ through another process in which the net heat absorbed by the system is $13.5 \mathrm{cal}$, then the net workdone by the system in the later case is $\left(1 \mathrm{cal}=4.2 \mathrm{J}\right)$

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

Two cylinders $A$ and $B$ of equal capacity are connected to each other via a stopcock. A contains an ideal gas at standard temperature $\left(T_1\right)$ and pressure. $B$ is empty. Then the entire system is thermally insulated. The stopcock is suddenly opened. After the gas reaches equilibrium the temperature $\left(T_2\right)$ of the gas measured. Which of the following is correct?

$1 \mathrm{gm}$ 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 $\left(L\right)=540 \mathrm{cal} {\mathrm{gm}}^{-1},1\mathrm{cal}=4.2 \mathrm{J}$)

An ideal monatomic gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $2V$ and a final pressure $P_i$. If the same gas is expanded adiabatically to a volume $2V$, the final pressure is $P_{\mathrm{a}}$. The ratio $\frac{P_{\mathrm{a}}}{P_{\mathrm{i}}}$ is
 

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:

For an adiabatic expansion of ideal gas, the value of $\frac{\mathrm{\Delta }p}{p}$ is equal to

One mole of an ideal monoatomic gas is taken round the cyclic process $\mathrm{ABCA}$ as shown in figure then

One mole of a monoatomic gas is brought from state $\text{'}A\text{'}$ to state $\text{'}B\text{'}$ along path $ACB.$ Temperature at $\text{'}A\text{'}$ is $\text{'}{T}_0\text{'}$ Heat absorbed along path $ACB$ is equal to

At $27°\mathrm{C}$ two moles of an ideal monoatomic gas occupy a volume $V\mathit{.}$ The gas expands adiabatically to a volume $2V\mathit{.}$ Calculate the final temperature of the gas.

[Given $2^{2/3}=1.59$]

A cyclic process $ABCA$ is shown in $P-T$ diagram. What would be its $P-V$ graph: