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

One mole of an ideal monoatomic gas is taken round the cyclic process ABCA as shown in fig. Calculate

(a) The work done by the gas.

b) The heat rejected by the gas in the path$CA$ and heat absorbed in the path $AB$.

(c) The net heat absorbed by the gas in the path $BC$.

One mole of monoatomic gas is carried along process $ABCDEA$ as shown in the diagram. Find the net work done by gas.

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 

How the first law of thermodynamics can be justified? Give an example in support of your answer.

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 $\simeq 2000 \mathrm{kJ} {\mathrm{kg}}^{-1}$]

State first law of thermodynamics.

Consider the following cycle (a-b-c) for ideal gas in the figure: b-c(adiabatic), c-a(isobaric), and a-b (isochoric). Calculate work done by the gas and heat absorbed by the gas for each path, a-b, b-c, c-a. What is the total work done and heat absorbed for the full cycle?

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 $=1\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$)

If $2000 \mathrm{J}$ of heat is supplied to gas at a pressure of $1.2 \times {10}^5 \mathrm{Pa}$, its volume increases from $2 \mathrm{l}$ to $7 \mathrm{l}$. Calculate the change in its internal energy.

$n$ 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.