First Law of Thermodynamics

Given below are two statements:

Statement I: If heat is added to a system, its temperature must increase.

Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.

In the light of the above statements, choose the correct answer from the options given below

A source supplies heat to a system at the rate of $1000 \mathrm{W}.$ If the system performs work at a rate of $200 \mathrm{W}.$ The rate at which internal energy of the system increases is

The amount of heat supplied to a gas in a system is equal to $1000 \mathrm{J}$, the system in return does $200 \mathrm{J}$ of work on the surrounding. Find change in internal energy of the gas.

If amount of heat given to the system be $80$ Joules and the amount of work done by the system is $-20 \mathrm{J}$ . If initial internal energy of the system is $250 \mathrm{J}$. Final internal energy of the system is

ideal gas expands from volume $V_1$to$V_2$,. This may be achieved by either of the three processes: isobaric, isothermal and adiabatic. Let $∆U$ be the change in internal energy of the gas, $Q$ be the quantity of heat added to the system and W be the work done by the gas. Identify which of the following statements is false for$∆U$?
 

$1 \mathrm{g}$ of water at atmospheric pressure has volume of $1 {\mathrm{cm}}^3$ and when boiled it becomes $1681 {\mathrm{cm}}^3$ of steam. The heat of vaporization of water is $540 \mathrm{cal} {\mathrm{g}}^{-1}$. Then the change in its internal energy in this process is 

An ideal gas is expanded adiabatically at an initial temperature of $300 \mathrm{K}$ so that its volume is doubled. The final temperature of the hydrogen gas is $\left(\gamma =1.4\right)$

In an insulated container of water is stirred with a rod to increase the temperature. Which of the following is true?

$1 \mathrm{kg}$ of water is heated from $40 °\mathrm{C}$ to $70 °\mathrm{C}$, if its volume remains constant, then the change in internal energy is (specific heat of water $=4148 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$)

$1.00 \mathrm{kg}$ of liquid water at $100°\mathrm{C}$ undergoes a phase change into steam at $100{}^{\circ }\mathrm{C}$ at $1.0$ atm (take it to be $1.00\times {10}^5 \mathrm{Pa}$). The initial volume of the liquid water was $1.00\times {10}^{-3} {\mathrm{m}}^3$ which is changed to $2.001 {\mathrm{m}}^3$ of steam. Find the change in the internal energy of the system.
[Use heat of vaporization $\simeq 2000 \mathrm{kJ} {\mathrm{kg}}^{-1}$]

In the diagram shown $Q_{\text{iaf }}=80\mathrm{cal}$ and $W_{\mathrm{ef}}=50$ cal. If $W=-30$ cal for the curved path $f$ value of $Q$ for path $fi$, will be

Which of the following is the correct equation?

A cube of side $5 \mathrm{cm}$ made of iron and having a mass of $1500 \mathrm{g}$ is heated from $25°\mathrm{C}$ to $400°\mathrm{C}$. The specific heat for iron is $0.12 \mathrm{cal} {\mathrm{g}}^{-1} °{\mathrm{C}}^{-1}$ and the coefficient of volume expansion is $3.5\times {10}^{-5} {}^{\circ }\mathrm{C}^{-1}$, the change in the internal energy of the cube is (atm pressure $=1\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$)

$n$ moles of an ideal gas is taken through a cyclic process $ABCD$. Pressure - density diagram of which is shown in adjacent figure. If molar mass of gas is $M$, what will be the work done by gas in cycle.

A heat engine used one mole of an ideal monatomic gas as a working substance. The engine can follow either cycle $A$ or cycle $B$ in the diagram. The ratio of the efficiencies of the cycles is $\left(\frac{{\mathrm{e}}_{\mathrm{A}}}{{\mathrm{e}}_{\mathrm{B}}}\right)=4.$ If the value of $e_{\mathit{A}}+e_{\mathit{B}}$ is $\frac{n}{4}.$ Find the value of $n.$

One mole of a monoatomic ideal gas follows a process $A\to B,$ as shown $\left(A\equiv V_0,3P_0\right.$ and $\left.B\equiv 5V_0,n{P}_0\right).$ The average molar heat capacity for the process is $\frac{13R}{6}.$ The value of $\text{'}n\text{'}$ on $P-$axis (see following figure) is

A cylindrical vessel is divided in two parts by a fixed partition which is perfectly heat conducting. The wall and piston are thermally insulated from surroundings. The left side contains $0.5$ moles of gas with $C_v=2R$ at temperature of $300 \mathrm{K}.$ The right side contains $4$ moles of a mixture of gases with $C_v=1.75R$ at same temperature of $300 K.$ The piston compresses slowly the right side from volume of $V_0$ to $\frac{V_0}{4}.$ Find the total change in internal energy of gases. (take $R=\frac{25}{3} S.I.$ unit and consider ideal gases only)

According to the first law of thermodynamics, $\mathrm{\Delta U}=\mathrm{q}+\mathrm{w}.$ In special cases the statement can be expressed in different ways. Which of the following is not a correct expression?

An ideal gas is allowed to expand freely against vacuum in a rigid insulated container. The gas undergoes

When heat is supplied to the system then $\Delta Q$ is ____ and $\Delta Q$ is ____ when heat is extracted from the system. Choose the appropriate option.