Internal Energy and First Law of Thermodynamics

If $\mathrm{\Delta H}$ is the change in enthalpy and $\mathrm{\Delta E},$ the change in internal energy accompanying a gaseous reaction, then

Internal energy and pressure of a gas per unit volume are related as:

$3$ moles of an ideal gas expands isothermally against a constant pressure of $2$ Pascal from $20 \mathrm{L}\text{ to} 60$ L.The amount of work involved is

The ratio K_p to K_c of a reaction is 24.63 L atm mol^–1 at 27°C. If heat of reaction at constant pressure is 98.8 kcal, calculate the heat of reaction (in kcal) at constant volume? (Report the value in the nearest integer)

(use $\mathrm{R}$ values $0.0821\mathrm{lit} \mathrm{atm} {\mathrm{mole}}^{-1}{\mathrm{k}}^{-1}$and $2\mathrm{X}{10}^{-3 }\mathrm{kcal} {\mathrm{mole}}^{-1}{\mathrm{k}}^{-1}$)

A gas is enclosed in a cylinder with a piston. Weights are added to the piston, giving a total mass of $2.20 \mathrm{kg}$. As a result, the gas is compressed and the weights are lowered $0.25 \mathrm{m}$. At the same time, $1.50 \mathrm{J}$ of heat is evolved from the system. Calculate the change in internal energy of the system and report the answer in the nearest integer value

The ratio K_p to K_c of a reaction is 24.63 L atm mol^–1 at 27°C. If heat of reaction at constant pressure is 98.6 kcal, what is the heat of reaction (in kcal)  at constant volume?

The specific heat of a certain substance is $0.86 \mathrm{J} {\mathrm{g}}^{-1} {\mathrm{K}}^{-1}$. Assuming ideal solution behavior, the energy required (in $\mathrm{J}$) to heat $10 \mathrm{g}$ of $1$ molal of its aqueous solution from $300 \mathrm{K}$ to $310 \mathrm{K}$ is closest to :

[Given: molar mass of the substance $=58 \mathrm{g} {\mathrm{mol}}^{-1}$; specific heat of water $=4.2 \mathrm{J} {\mathrm{g}}^{-1} {\mathrm{K}}^{-1}$]

$1.0 \mathrm{mol}$ of a mono-atomic ideal gas is expanded from state $\left(1\right)$ to state $\left(2\right)$ as shown in the figure. Calculate the work done for the expansion of gas in Joules from state $\left(1\right)$ to state $\left(2\right)$ at $298 \mathrm{K}$.

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

A thermally insulated rigid container of $1 \mathrm{L}$ volume contains a diatomic ideal gas at room temperature. A small paddle installed inside the container is rotated from the outside, such that the pressure rises by ${10}^5 \mathrm{Pa}$. The change in internal energy is close to

Find the change in the internal energy $\left(\mathrm{\Delta U}\right)$ of a closed system, when $\text{'}\mathrm{w}\text{'}$ denotes the  amount of work done by the system and $\text{'}\mathrm{q}\text{'}$ amount of heat is supplied to the system.

Which factors affect the internal energy ?

What do you mean by the internal energy of a substance?

One mole of an ideal gas at $300 \mathrm{K}$ is expanded isothermally from an initial volume of $1$ $\mathrm{Litres}$ to $10$ $\mathrm{litres}$. The $∆\mathrm{U}$ for this process is ($\mathrm{R}=$$2$ $\mathrm{cal} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$)

$∆\mathrm{U}=\mathrm{q}+\mathrm{W}$ is mathematical expression for

A sample of gas absorbs $4000 \mathrm{kJ}$ of heat.

A sample of gas absorbs $4000 KJ$ of heat.

Suppose that in addition to absorption of heat by the sample, the surroundings does $2000 KJ$ of work on the sample, what is $∆\mathrm{U}$?

A sample of gas absorbs $4000 \mathrm{kJ}$ of heat. If volume remains constant, what is $∆\mathrm{U}$?

In the reaction, ${\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)⟶2\mathrm{HCl}\left(\mathrm{g}\right)$ $\mathrm{\Delta H}=-184\mathrm{kJ}$ if $2$ moles of ${\mathrm{H}}_2$ react with $2$ moles of ${\mathrm{Cl}}_2$, then $∆\mathrm{U}$ is equal to