Fundamentals of Thermodynamics

A piece of metal weighing $100 \mathrm{g}$ is heated to $80°\mathrm{C}$ and dropped into $1 \mathrm{kg}$ of cold water in an insulated container at $15°\mathrm{C}$. If the final temperature of the water in the container is $15.69°\mathrm{C}$, the specific heat of the metal in $\mathrm{J}/\mathrm{g}°\mathrm{C}$. is

When equal volumes of Helium and Neon at same temperature and pressure are mixed, the ratio ${\mathrm{C}}_{\mathrm{p}}:{\mathrm{C}}_{\mathrm{v}}$ of the mixture equals:

Which energy is a part of mechanical energy?

A heat pump is used to draw water from a well. The temperature of the water is $15°\mathrm{C}$ and that of the atmosphere is $40°\mathrm{C}$. If the amount of water drawn is $10 \mathrm{kg}$ from a depth of $12 \mathrm{m}$, calculate the amount of heat supplied to the well in kJ.

Express your answer up to nearest integer value.

The process in which the value of $∆\mathrm{U} = 0$ is:

The quantity of heat (in $J$) required to raise the temperature of $1.0\mathit{ }kg$ of ethanol from $293.45 K$ to the boiling point and then change the liquid to vapor at that temperature is closest to [Given, boiling point of ethanol $351.45 K$. Specific heat capacity of liquid ethanol $2.44\mathit{ }J\mathit{ }{g}^{-1} K^{-1}$. Latent heat of vaporisation of ethanol $855 J{g}^{-1}$ ]

An ideal monoatomic gas is subjected to following change.

If $\mathrm{R}$ is the gas constant then the molar heat capacity of the gas for the process is,

If we place $0.5 \mathrm{g}$ Lithium metal in coffee cup calorimeter that already contains $75 \mathrm{ml}$ of water. The specific heat capacity of reaction mixture is $4{\mathrm{Jg}}^{-1} {\mathrm{K}}^{-1}$. Temperature of water is increased from $22°\mathrm{C}$ to $72°\mathrm{C}$. Then find $△\mathrm{H}$ for the reaction.

$2\mathrm{Li}\left(\mathrm{s}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\to 2\mathrm{LiOH}\left(\mathrm{aq}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)$

The internal energy $\left(\mathrm{U}\right)$ of an ideal gas is plotted against volume for a cyclic process $\mathrm{ABCDA}$, as shown in the figure.

The temperature of the gas at $\mathrm{B}$ and $\mathrm{C}$ are $500 \mathrm{K}$ and $300 \mathrm{K}$, respectively. The heat absorbed by the gas (in $\mathrm{cal}/\mathrm{mol}$) in this cyclic process, is :

How much heat will be required at constant volume at $727°\mathrm{C}$ to form $1.28 \mathrm{kg}$ of ${\mathrm{CaC}}_2$ from $\mathrm{CaO}\left(\mathrm{s}\right)$ and $\mathrm{C}\left(\mathrm{s}\right)$

Given: ${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^{\circ }(\mathrm{CaO},\mathrm{s})=-152\mathrm{kcal}/\mathrm{mol}$

${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^{\circ }\left({\mathrm{CaC}}_2,\mathrm{s}\right)=-14\mathrm{kcal}/\mathrm{mol}$

${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^{\circ }(\mathrm{CO},\mathrm{g})=-24\mathrm{kcal}/\mathrm{mol}$

one mole of an ideal gas at $300 \mathrm{K}$ is expanded isothermally from an initial volume of $1 \mathrm{litre}$to $10 \mathrm{litre}$. The $\mathrm{\Delta U}$ for this process is: $\left(\mathrm{R}=2 \mathrm{cal} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right)$

An ideal gas initially at temperature ${\mathrm{T}}_1$ with $\mathrm{\gamma }=5/3$ expands adiabatically into vacuum to double its volume. The final temperature ${\mathrm{T}}_2$ is given by:

A water heater, operating on a hydrocarbon fuel heats water flowing at the rate of $5 \mathrm{kg}$ per minute, from $27°\mathrm{C}$ to $77°\mathrm{C}$. If the heat of combustion of hydrocarbon is $20,000 \mathrm{J}/\mathrm{g}$, how much fuel in $\mathrm{g}$ is consumed per minute? (Specific heat of water is $4200 \mathrm{J}/\mathrm{Kg}-\mathrm{K})$

A diatomic ideal gas changes its state from $\mathrm{A}$ to $\mathrm{B}$ as shown in the figure.

Choose the correct $\mathrm{U}$ versus $\mathrm{V}$ graph: (where $\mathrm{U}$ is internal energy of the gas)

One gram sample of ${\mathrm{NH}}_4{\mathrm{NO}}_3$ is decomposed in a bomb calorimeter temperature increases by $6.12 \mathrm{K}$. The heat capacity of the system is $1.23 \mathrm{kJ}/\mathrm{gram}-\mathrm{degree}$. What is the molar heat of decomposition for ${\mathrm{NH}}_4{\mathrm{NO}}_3$?

Which of the following statement is INCORRECT ?

The internal energy of an ideal gas increases during an isothermal process when the gas is :-

A reaction proceeds through two paths $\mathrm{I}$ and $\mathrm{II}$ to convert $\mathrm{X}\to \mathrm{Z}$.

What is the correct relationship between $\mathrm{Q}$, ${\mathrm{Q}}_1$ and ${\mathrm{Q}}_2$ ?

The entropy change accompanying the heating of one mole of helium gas, assuming ideal behaviour, from a temperature of $250 \mathrm{K}$to a temperature of $1000 \mathrm{k}$ at constant pressure, in $\mathrm{ }\mathrm{cal}\mathrm{ }{\mathrm{K}}^{-1}{\mathrm{mole}}^{-1}$ is ( Give answer to the nearest integer after rounding off.)

$\left(\ln 10=2.3,\log 2=0.3\right)\mathrm{ }$

$\left(\mathrm{R}=2\mathrm{ }\mathrm{Cal} {\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}\right)$

$200 \mathrm{J}$ of heat is provided to the system. Work done on the system is $20 \mathrm{J}$. What is the change in internal energy?