First law and internal energy

Ten moles of an ideal monoatomic gas, initially in state $\boldsymbol a$ at atmospheric pressure and temperature $T_a=27^\circ$C, is enclosed in a metal cylinder of volume $V_0$ fitted with a frictionless piston. The gas is suddenly compressed to state $\boldsymbol b$ with volume $V_0/3$. Now, keeping the piston stationary, the cylinder is submerged in a water bath of temperature $11^\circ$C until the gas reaches the temperature of the water bath, which is denoted as state $\boldsymbol c$. Finally, while still in the water bath, the piston is brought slowly to its initial position, which is denoted as state $\boldsymbol f$. If $R$ is universal gas constant, then the correct option(s) is/are:
[Given: $9^{1/3}=2.08$]

5 moles of unknown gas is heated at constant volume from 10 °C to 20 °C. The molar specific heat of this gas at constant pressure $c_p=8$ cal/mol.°C and $R=8.36$ J/mol.°C. The change in the internal energy of the gas is ________ calorie.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Statement I: Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U=nC_v\left(T_f-T_i\right)=\dfrac{nR}{\gamma-1}\left(T_f-T_i\right)$, where $\gamma=\dfrac{C_p}{C_v}$, $T_i$ = initial temperature, $T_f$ = final temperature.

Statement II: Relation between degree of freedom $f$ and $\gamma\ (=C_p/C_v)$ is $\left(\gamma=1+\dfrac2f\right)$

Choose the correct answer from the options given below

Consider the following statements:

A. Zeroth law of thermodynamics gives concept of temperature

B. First law of thermodynamics gives concept of internal energy

C. In isothermal expansion of ideal gas, $\Delta Q\ne\Delta W$

D. Product of intensive and extensive variables is extensive

E. The ratio of any extensive variable to mass will be an extensive variable

Choose the correct combination of statements from the options given below:

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is 4 cm². The gas is heated slowly to raise the temperature by 1.2 °C during which the piston moves by 25 mm. The amount of heat supplied to the gas is ________ J.

(Atmospheric pressure = 100 kPa, R = 8.3 J/mol. K) (Neglect mass of the piston)

One mole of a monatomic ideal gas undergoes the cyclic process J→K→L→M→J, as shown in the P-T diagram.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

[$\mathcal{R}$ is the gas constant.]

A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas ($\gamma = 5/3$) and one mole of an ideal diatomic gas ($\gamma = 7/5$). Here, $\gamma$ is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of 66 Joule when heated at constant pressure. The change in its internal energy is _____ Joule.

List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

Which one of the following options is correct?

A monoatomic gas performs a work of $\dfrac Q4$ where Q is the heat supplied to it. The molar heat capacity of the gas will be ______ R during this transformation.

Where R is the gas constant.

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by :

(R = universal gas constant)

A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The workdone by the gas during the part CA is :

7 mol of a certain monoatomic ideal gas undergoes a temperature increase of 40K at constant pressure. The increase in the internal energy of the gas in this process is :

(Given R = 8.3 JK$^{-1}$ mol$^{-1}$)

At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be ______ J.

An ideal gas undergoes a four step cycle as shown in the $P-V$ diagram below. During this cycle, heat is absorbed by the gas in

The value of $\dfrac{T_R}{T_0}$ is

The value of $\dfrac{Q}{RT_0}$ is

A thermally isolated cylindrical closed vessel of height 8 m is kept vertically. It is divided into two equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass 8.3 kg. Thus the partition is held initially at a distance of 4 m from the top, as shown in the schematic figure below. Each of the two parts of the vessel contains 0.1 mole of an ideal gas at temperature 300 K. The partition is now released and moves without any gas leaking from one part of the vessel to the other. When equilibrium is reached, the distance of the partition from the top (in m) will be ______ (take the acceleration due to gravity $= 10\ \mathrm{m\,s^{-2}}$ and the universal gas constant $= 8.3\ \mathrm{J\,mol^{-1}K^{-1}}$).

If the process carried out on one mole of monatomic ideal gas is as shown in figure in the $PV$-diagram with $P_0V_0 = \frac13RT_0$, the correct match is,

If the process on one mole of monatomic ideal gas is as shown in the $TV$-diagram with $P_0V_0 = \frac13RT_0$, the correct match is,

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V$ is the volume and $T$ is the temperature). Which of the statements below is (are) true?