1st Law of Thermodynamics

Q.

What is closed system in thermodynamics?

Q.

In a certain thermodynamic process, the pressure of a gas depends on its volume as $k{V}^3$. The work done when the temperature changes from $100°C$ to $300°C$ will be $\_\_\_\_\_\_\_\_nR$, where $n$ denotes number of moles of a gas.

Q.

What is $∆\mathrm{U}$ in adiabatic process?

Q. The change in internal energy of a system that has absorbed $2\text{kcal}$ of heat and does $500\text{J}$ of work is

1. $6400\text{J}$
2. $5400\text{J}$
3. $7860\text{J}$
4. $8900\text{J}$

Q.

Is the isochoric process reversible?

Q. An ideal gas undergoes an expansion from a state with temperature $T_1$ and volume $V_1$ through three different polytropic process A, B and C as shown in the $P-V$ diagram. If $|\Delta E_A|,|\Delta E_B|$ and $|\Delta E_C|$ be the magnitude of changes in internal energy along the three paths respectively, then

1. $|\Delta E_A|<|\Delta E_B|<|\Delta E_C|$ if temperature in every process decreases
2. $|\Delta E_A|>|\Delta E_B|>|\Delta E_C|$ if temperature in every process decreases
3. $|\Delta E_A|>|\Delta E_B|>|\Delta E_C|$ if temperature in every process increases
4. $|\Delta E_B|<|\Delta E_A|<|\Delta E_C|$ if temperature in every process increases

Q. The figure shows two processes, $1$ and $2$ for a given sample of a gas. If $\Delta Q_1,\Delta Q_2$ are the amounts of heat absorbed by the system in the two cases and $\Delta U_1,\Delta U_2$ are changes in internal energies respectively, then

1. $\Delta Q_1=\Delta Q_2;\Delta U_1=\Delta U_2$
2. $\Delta Q_1>\Delta Q_2;\Delta U_1>\Delta U_2$
3. $\Delta Q_1<\Delta Q_2;\Delta U_1<\Delta U_2$
4. $\Delta Q_1>\Delta Q_2;\Delta U_1=\Delta U_2$.

Q. Which of the following is an intensive property?

1. Mass
2. Surface tension
3. Volume
4. None of these

Q. A figure show a closed cycle for a gas. The change in internal energy along the path $ca$ is $-160\text{J}$. The energy transferred to the gas as heat is $200\text{J}$ along path $ab$ and $40\text{J}$ along path $bc$. What is the ratio of work done by the gas along the path $abc$ and $ab$?

1. 1 : 1
2. 2 : 1
3. 1 : 2
4. 3 : 2

Q. The $P-V$ diagram of $2\text{gm}$ of helium gas for a certain process is shown in the figure. Find the amount of heat given to the gas during the process ?

1. $4P_0{V}_0$
2. $6P_0{V}_0$
3. $4.5P_0{V}_0$
4. $2P_0{V}_0$

Q. The figures given below show different processes (relating pressure $P$ and volume $V$) for a given amount for an ideal gas. $\Delta W$ is work done by the gas and $\Delta Q$ is heat absorbed by the gas.

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ 1.\text{In Fig}\left(i\right)& \left(p\right)\Delta Q>0\\ 2.\text{In Fig}\left(ii\right)& \left(q\right)\Delta W<0\\ 3.\text{In Fig}\left(iii\right)& \left(r\right)\Delta Q<0\\ 4.\text{In Fig}\left(iv\right)& \left(s\right)\Delta W>0\end{array}$

1. $1\to (p,r)2\to q,3\to (p,r),4\to (p,r)$
2. $1\to (p,r),2\to s,3\to (p,s),4\to (p,r)$
3. $1\to (p,s),2\to s,3\to (p,s),4\to (q,r)$
4. $1\to (p,s),2\to p,3\to (p,r),4\to (p,s)$
   

Q. A sample of ideal gas at ${100}^{\circ }\text{C}$ and normal pressure $(1.03\times {10}^5{\text{Nm}}^{-2})$ absorbs $54\text{cal}$ of heat energy at constant pressure. If the volume of the gas increases by $167\text{cc}$, the change in internal energy of the sample is :

1. $+104.4\text{J}$
2. $+208.8\text{J}$
3. $-84.5\text{J}$
4. $-242.6\text{J}$

Q. A perfect gas goes from state $A$ to another state $B$ by absorbing $8\times {10}^5\text{J}$ of heat and doing $6.5\times {10}^5\text{J}$ of external work. The change in internal energy will be

1. $1450\text{kJ}$
2. $150\text{kJ}$
3. $15\text{kJ}$
4. $145\text{kJ}$

Q. A figure show a closed cycle for a gas. The change in internal energy along the path $ca$ is $-160\text{J}$. The energy transferred to the gas as heat is $200\text{J}$ along path $ab$ and $40\text{J}$ along path $bc$. What is the ratio of work done by the gas along the path $abc$ and $ab$?

1. 1 : 1
2. 2 : 1
3. 1 : 2
4. 3 : 2

Q. The first law of thermodynamics
1. is a re-statement of the law of conservation of energy when applied to thermodynamic systems.
2. is the basis for the definition of internal energy.
3. is basis for the definition of temperature.

1. 1 and 2 are correct
2. Only 1 is correct
3. Only 2 is correct
4. Both 2 and 3 are correct

Q.

A system is any specified portion of matter which is separated from the rest of the universe with a definite boundary. (T/F)

1. True

2. False

Q. The first law of thermodynamics
1. is a re-statement of the law of conservation of energy when applied to thermodynamic systems.
2. is the basis for the definition of internal energy.
3. is basis for the definition of temperature.

1. 1 and 2 are correct
2. Only 1 is correct
3. Only 2 is correct
4. Both 2 and 3 are correct

Q. In the figure shown below, $ABCD$ is a cyclic process,


Statement 1: Work is done on the system.
Statement 2: Heat is drawn from the system.

1. Statement 1 is true, statement 2 is false
2. Statement 1 is false, statement 2 is true
3. Both statement 1 and 2 are true
4. Both statement 1 and 2 are false

Q. The figures given below show different processes (relating pressure $P$ and volume $V$) for a given amount for an ideal gas. $\Delta W$ is work done by the gas and $\Delta Q$ is heat absorbed by the gas.

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ 1.\text{In Fig}\left(i\right)& \left(p\right)\Delta Q>0\\ 2.\text{In Fig}\left(ii\right)& \left(q\right)\Delta W<0\\ 3.\text{In Fig}\left(iii\right)& \left(r\right)\Delta Q<0\\ 4.\text{In Fig}\left(iv\right)& \left(s\right)\Delta W>0\end{array}$

1. $1\to (p,r)2\to q,3\to (p,r),4\to (p,r)$
2. $1\to (p,r),2\to s,3\to (p,s),4\to (p,r)$
3. $1\to (p,s),2\to s,3\to (p,s),4\to (q,r)$
4. $1\to (p,s),2\to p,3\to (p,r),4\to (p,s)$
   

Q. A system has absorbed $5\text{kcal}$ of heat and does $200\text{J}$ of work. The change in internal energy of the system is

1. $20.8\text{J}$
2. $20.8\text{kJ}$
3. $208\text{J}$
4. $2.08\text{kJ}$

Q. During the thermodynamic process shown in figure for an ideal gas.

1. $\Delta T=0$
2. $\Delta Q=0$
3. $W<0$
4. $\Delta U>0$

Q. A gas is compressed at a constant pressure of $50{\text{N/m}}^2$ from a volume of $10{\text{m}}^3$ to a volume of $4{\text{m}}^3$. Heat of $100\text{J}$ is then added to the gas by heating it at constant volume. Its internal energy is

1. Decreased by $200\text{J}$
2. Increased by $200\text{J}$
3. Decreased by $400\text{J}$
4. Increased by $400\text{J}$

Q. The figure shows two processes, $1$ and $2$ for a given sample of a gas. If $\Delta Q_1,\Delta Q_2$ are the amounts of heat absorbed by the system in the two cases and $\Delta U_1,\Delta U_2$ are changes in internal energies respectively, then

1. $\Delta Q_1=\Delta Q_2;\Delta U_1=\Delta U_2$
2. $\Delta Q_1>\Delta Q_2;\Delta U_1>\Delta U_2$
3. $\Delta Q_1<\Delta Q_2;\Delta U_1<\Delta U_2$
4. $\Delta Q_1>\Delta Q_2;\Delta U_1=\Delta U_2$.

Q. The change in internal energy of a system that has absorbed $2\text{kcal}$ of heat and does $500\text{J}$ of work is

1. $6400\text{J}$
2. $5400\text{J}$
3. $7860\text{J}$
4. $8900\text{J}$

Q.

An ideal monoatomic gas is taken round the cycle ABCA as shown in the Fig. 17.9 The work done during the cycle is

1. zero

2. 3 PV

3. 6 PV

4. 9 PV

Q. The work done in which of the following processes is zero

1. Isothermal process
2. Adiabatic process
3. Isochoric process
4. None of these

Q. One mole of an ideal monatomic gas has initial temperature $T_0$ is made to go through the cycle $abca$ as shown in the given figure. If $U$ denotes the internal energy, then choose the correct alternative.

1. $U_c>U_b>U_a$
2. $U_c-U_b=3R{T}_0$
3. $U_c-U_a=\frac{9R{T}_0}{2}$
4. $U_b-U_a=\frac{3R{T}_0}{2}$

Q. Following figure shows on adiabatic cylindrical container of volume V_o divided by an adiabatic smooth piston (area of cross-section = A) in two equal parts. An ideal gas is at pressure P₁ and temperature T₁ in left part and gas at pressure P₂ and temperature T₂ in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose x = displacement of the piston)

1. $P_2$
2. $P_1$
3. $\frac{P_1(\frac{V_0}{2}{)}^{\gamma }}{{(\frac{V_0}{2}+Ax)}^{\gamma }}$
4. $\frac{P_2(\frac{V_0}{2}{)}^{\gamma }}{{(\frac{V_0}{2}+Ax)}^{\gamma }}$

Q. A perfect gas goes from a state $A$ to state $B$ by absorbing $8\times {10}^5\text{J}$ and by doing $6.5\times {10}^5\text{J}$ of external work. It is taken from same initial state $A$ to final state $B$ in another process in which it absorbs ${10}^5\text{J}$ of heat, then work done in the second process

1. on gas is ${10}^5\text{J}$
2. on gas is $0.5\times {10}^5\text{J}$
3. by gas is ${10}^5\text{J}$
4. by gas is $0.5\times {10}^5\text{J}$

Q. A gas is undergoing a cyclic process as shown in figure, where $P_0=2\text{bar}$ and $V_0=7{\text{m}}^3$. Find the workdone ($W$) by the gas and heat ($Q$) released by the gas in one cycle.

1. $44\times {10}^5\text{J}$, $-44\times {10}^5\text{J}$
2. $-44\times {10}^5\text{J}$, $44\times {10}^5\text{J}$
3. $88\times {10}^5\text{J}$, $44\times {10}^5\text{J}$
4. $-88\times {10}^5\text{J}$, $88\times {10}^5\text{J}$