Thermodynamics

5 moles of unknown gas is heated at constant volume from 10 $^\circ$C to 20 $^\circ$C. The molar specific heat of this gas at constant pressure $c_p=8$ cal/mol. $^\circ$C and $R=8.36$ J/mol.$^\circ$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 $\Delta U = nC_v(T_f - T_i) = \frac{nR}{\gamma-1}(T_f - T_i)$, where $\gamma = \frac{C_p}{C_v}$, $T_i$ = initial temperature, $T_f$ = final temperature. Statement II: Relation between degree of freedom $f$ and $\gamma\ (= C_p/C_v)$ is $\left(\gamma = 1 + \frac{2}{f}\right)$. 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:

An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3$ = constant. The coefficient of volume expansion of the gas is ______.

Initial pressure and volume of a monoatomic ideal gas are $P$ and $V$. The change in internal energy of this gas in adiabatic expansion to volume $V_{final}=27V$ is ______ J.

An amount of ice of mass $10^{-3}$ kg and temperature $-10^\circ$C is transformed to vapour of temperature $110^\circ$C by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice $=2100$ J kg$^{-1}$K$^{-1}$, specific heat of water $=4180$ J kg$^{-1}$K$^{-1}$, specific heat of steam $=1920$ J kg$^{-1}$K$^{-1}$, Latent heat of ice $=3.35\times10^{5}$ J kg$^{-1}$ and Latent heat of steam $=2.25\times10^{6}$ J kg$^{-1}$)

Given are statements for certain thermodynamic variables, (A) Internal energy, volume (V) and mass (M) are extensive variables. (B) Pressure (P), temperature (T) and density ($\rho$) are intensive variables. (C) Volume (V), temperature (T) and density ($\rho$) are intensive variables. (D) Mass (M), temperature (T) and internal energy are extensive variables. Choose the correct answer from the options given below :

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J, then the mass of the bullet is ____ grams. (Latent heat of fusion of lead $=2.5\times10^4\ \mathrm{J\,kg^{-1}}$ and specific heat capacity of lead $=125\ \mathrm{J\,kg^{-1}K^{-1}}$)

Match the LIST-I with LIST-II. LIST-I: A. Pressure varies inversely with volume of an ideal gas. B. Heat absorbed goes partly to increase internal energy and partly to do work. C. Heat is neither absorbed nor released by a system. D. No work is done on or by a gas. LIST-II: I. Adiabatic process II. Isochoric process III. Isothermal process IV. Isobaric process. Choose the correct answer from the options given below: