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

One mole of an ideal gas (not necessarily monoatomic) is subjected to the following sequence of steps.
(a) It is heated at constant volume from $298 \mathrm{K} \text{to} 373 \mathrm{K}$
(b) It is expanded freely into a vacuum to double volume.
(c) It is cooled reversibly at constant pressure to $298 \mathrm{K}$.
Calculate $\mathrm{q}, \mathrm{w}, ∆\mathrm{U}$ and $∆\mathrm{H}$ for the overall process.​

$0.5 \mathrm{mol}$ of diatomic gas at $27°\mathrm{C}$ is heated at constant pressure so that its volume is tripled. If $\mathrm{R}=8.3{\mathrm{Jmole}}^{-1}{{\mathrm{k}}^{-}}^1$ then work done is 

When an idea gas in a cylinder was compressed isothermally by a piston, the work done on the gas found to be $1.5\times {10}^4 \mathrm{J}$. During this process about

One mole of ${\mathrm{O}}_2$​ gas having a volume equal to $22.4 \mathrm{L}$ at $0°\mathrm{C}$ and $1\mathrm{atm}$ pressure is compressed isothermally so that its volume reduces to $11.2 \mathrm{L}$. The work done in this process is then

$10 {\mathrm{dm}}^3$ of ${\mathrm{O}}_2$ at $101.325 \mathrm{kPa}$ and $298 \mathrm{K}$ is heated to $348 \mathrm{K}$. Calculate the heat absorbed, $∆\mathrm{H}$ and $∆\mathrm{U}$ for this process.at

$1.$ Constant pressure

$2.$Constant Volume

Calculate the internal energy of a gas that absorbs $400 \mathrm{J}$ of heat and expands from$1\times {10}^{-3} {\mathrm{m}}^3$ to $3\times {10}^{-3} {\mathrm{m}}^3$ against a constant pressure 1 bar. 

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

For the reaction at $25°\mathrm{C}$,

${\mathrm{NH}}_3\left(\mathrm{g}\right)\to \frac{1}{2}{\mathrm{N}}_2\left(\mathrm{g}\right)+\frac{3}{2}{\mathrm{H}}_2\left(\mathrm{g}\right); ∆{\mathrm{H}}^{°}=11.04 \mathrm{kcal}$

Calculate ${\mathrm{\Delta U}}^{°}$ for the reaction at the given temperature.

(Note: Report your answer after multiplying with 100 and rounding up to 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 $=4.2 \mathrm{J} {\mathrm{g}}^{-1} {\mathrm{K}}^{-1}$]

$10$ moles of an ideal gas expands isothermally and reversibly from the pressure $10 \mathrm{atm}$ to $2 \mathrm{atm}$ at $300 \mathrm{K}$. What is the largest mass in Kg, which can be lifted through a height of $1$ meter in this expansion?

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.

If the work is done by the system,${\mathrm{w}}_{\mathrm{ad}}$ will be negative because _____ .

According to IUPAC conventions work done on the surroundings is :

Which of the following statements are correct as per IUPAC sign convention ?