Heat and Work

Q. In the cyclic process shown in P-V diagram, the magnitude of the work done is

1. $\pi {\left(\frac{P_2-P_1}{2}\right)}^2$
2. $\pi {\left(\frac{V_2-V_1}{2}\right)}^2$
3. $\frac{\pi }{4}(P_2-P_1)(V_2-V_1)$
4. $\pi (V_2-V_1{)}^2$

Q. Which of the following statements is incorrect?

1. For an isothermal process, dT = 0.
   Where, T is the temperature of the system.
2. For an isobaric process, dP = 0.
   Where. P is the pressure of the system.
3. For an Isochoric process, dV = 0.
   Where, V is the volume of the system.
4. For an adiabatic process, dW = 0,
   where, W is the work done in the process

Q. 6 g of $O_2$ gas at STP is expanded against atmosphere so that the volume is doubled. Thus, the work done is:

1. 22.4 L atm
2. - 4.2 L atm
3. 5.6 L atm
4. 11.2 L atm

Q. Identify the pair of intensive properties among the following.

1. Enthalpy and temperature
2. Volume and temperature
3. Enthalpy and volume
4. Temperature and refractive index

Q. An ideal monatomic gas is taken round the cycle ABCD as shown in the figure. The work done during the cycle is:

1. $2pV$
2. zero
3. $pV$
4. $\frac{1}{2}pV$

Q. A gas undergoes change from state A to state B. In this process, the heat absorbed and work done by the gas is 5J and 8J, respectively. Now gas is brought back at A by another process during which 3J of heat is evolved. In this reverse process of B to A:

1. 10 J of the work will be done by the gas.
2. 6 J of the work will be done by the gas.
3. 10 J of the work will be done by the surrounding on gas.
4. 6 J of the work will be done by the surrounding on gas

Q. Calculate the total work done along the path 'ABCD' (as shown in figure) for a one mole of monoatomic gas.

1. $W=P_0{V}_0(1+ln2)$
2. $W=-RTln2$
3. $W=-P_0{V}_0(1+ln2)$
4. $W=-P_0{V}_{0}ln2$

Q. A heating coil is immersed in a 100 g sample of $H_{2}O\left(l\right)$ at 1 atm and ${100}^{\circ }C$ in a closed vessel. In this heating process, 60% of the liquid is converted in to gaseous form at constant pressure of 1 bar. Densities of liquid and gaseous water under these condition are 1000$kg/m^3,0.60kg/m^3$ respectively. magnitude of the work done for the process is :

1. None of these
2. 4997 J
3. 3970 J
4. 9994 J

Q. Which of the following are extensive properties?

1. Volume and enthalpy
2. Volume and temperature
3. Volume and specific heat
4. Pressure and temperature

Q. One mole of an ideal gas $(C_v=20J{K}^{-1}mo{l}^{-1})$ initially at STP is heated at constant volume to twice the initial temperature. For the process, work done ($w$) and $q$ will be :

1. $w=0;q=5.46kJ$
2. $w=0;q=0$
3. $w=-5.46kJ;q=5.46kJ$
4. $w=5.46kJ;q=5.46kJ$

Q.

For the process to occur under adiabatic conditions, the correct condition is:
(i) $\Delta T=0$
(ii) $\Delta p=0$
(iii) q = 0
(iv) w = 0

Q. 16 g oxygen gas expands at STP to occupy double of its original volume. The work done during the process is

1. -260.2 cal
2. 260.2 kcal
3. -272.8 cal
4. 272.8 kcal

Q. $56\text{g}$ of iron reacts with dilute $H_{2}S{O}_4$ at $30{}^o\text{C}$. Work done (in cal) in:
$\left(I\right)$ a closed vessel of fixed volume
$\left(II\right)$ an open vessel
is:
(given molar mass of $Fe$ is $56\text{g/mol}$)

1. $\begin{array}{cc}I& II\\ 0& -606\end{array}$
2. $\begin{array}{cc}I& II\\ 0& 0\end{array}$
3. $\begin{array}{cc}I& II\\ -600& 600\end{array}$
4. $\begin{array}{cc}I& II\\ 0& -303\end{array}$

Q. 1 mole of an ideal gas, initially at 400 K and 10 atm is first expanded at constant pressure till the volume is doubled. Then the gas is made to undergo an isochoric process, in which its temperature is found to decrease. In the last step, the gas was compressed reversibly and adiabatically to its initial state. Determine the net work involved in this cyclic process (in terms of R). Given, $C_V$ for gas $=1.5\text{R},(4{)}^{-1/3}=0.63$. If $|W|=\text{2 R}\times \text{z}$, what is the value of $\text{z}$?

Q. $16\text{g}$ oxygen gas expands at $STP$ to occupy double of its original volume. Calculate the work done during the process is:

1. $260\text{kcal}$
2. $180\text{kcal}$
3. $130\text{kcal}$
4. $-272.8\text{kcal}$

Q. Assign the sign of work done (based on SI convention) in the following chemical changes taking place against the external atmospheric pressure:
$\left(I\right)N_2\left(g\right)+3H_2\left(g\right)\to 2N{H}_3\left(g\right)$
$\left(II\right)N{H}_{4}HS\left(s\right)\to N{H}_3\left(g\right)+H_{2}S\left(g\right)$
$\left(III\right)C\left(s\right)+C{O}_2\left(g\right)\to 2CO\left(g\right)$
$\left(IV\right)C_2{H}_6\left(g\right)+3.5O_2\left(g\right)\to 2C{O}_2\left(g\right)+3H_{2}O\left(l\right)$

1. I II III IV
   $+--+$
2. I II III IV
   $++--$
3. I II III IV
   $-+0+$
4. I II III IV
   $+-0-$

Q. During an adiabatic reversible change, the density becomes $\frac{1}{16}$th of the initial value. Then find $\frac{P_1}{P_2}$ is : $(\gamma =1.5)$

1. $16$
2. $4$
3. $32$
4. $64$

Q. Closed systems can exchange which of the following with the surroundings?

1. Heat
2. Matter
3. Heat and Matter
4. Neither heat nor matter

Q. In the figure , the net amount of work done will be:

1. Positive
2. Negative
3. Zero
4. Infinity

Q. Which of the following represents the correct relation between $K_{sp}\left(AgCl\right)$ and standard reduction potential of $Ag|AgCl\left(\text{saturated}\right)\text{in}KCl$ electrode?

1. $E_{C{l}^{-}/AgCl/Ag}^0=\frac{RT}{F}ln{K}_{sp}$
2. $E_{C{l}^{-}/AgCl/Ag}^0=\frac{RT}{F}ln{K}_{sp}-E_{A{g}^{+}/Ag}^0$
3. $E_{C{l}^{-}/AgCl/Ag}^0=\frac{RT}{F}ln{K}_{sp}+E_{A{g}^{+}/Ag}^0$
4. $E_{C{l}^{-}/AgCl/Ag}^0=E_{A{g}^{+}/Ag}^0$

Q. $56\text{g}$ of iron reacts with dilute $H_{2}S{O}_4$ at $30{}^o\text{C}$. Work done (in cal) in:
$\left(I\right)$ a closed vessel of fixed volume
$\left(II\right)$ an open vessel
is:
(given molar mass of $Fe$ is $56\text{g/mol}$)

1. $\begin{array}{cc}I& II\\ 0& -606\end{array}$
2. $\begin{array}{cc}I& II\\ 0& 0\end{array}$
3. $\begin{array}{cc}I& II\\ -600& 600\end{array}$
4. $\begin{array}{cc}I& II\\ 0& -303\end{array}$

Q. Calculate the total work done along the path 'ABCD' (as shown in figure) for a one mole of monoatomic gas.

1. $W=-RTln2$
2. $W=-P_0{V}_0(1+ln2)$
3. $W=P_0{V}_0(1+ln2)$
4. $W=-P_0{V}_{0}ln2$

Q. One mole of an ideal gas $(C_v=20J{K}^{-1}mo{l}^{-1})$ initially at STP is heated at constant volume to twice the initial temperature. For the process, work done ($w$) and $q$ will be :

1. $w=0;q=5.46kJ$
2. $w=0;q=0$
3. $w=-5.46kJ;q=5.46kJ$
4. $w=5.46kJ;q=5.46kJ$

Q.

For the reaction $C_2{H}_4\left(g\right)+3O_2\left(g\right)\to 2C{O}_2\left(g\right)+2H_{2}O\left(l\right)$, the difference between enthalpy change and internal energy change is:

1. $-RT$
2. $+RT$
3. $-2RT$
4. $+2RT$

Q. A heating coil is immersed in a 100 g sample of $H_{2}O\left(l\right)$ at 1 atm and ${100}^{\circ }C$ in a closed vessel. In this heating process, 60% of the liquid is converted in to gaseous form at constant pressure of 1 bar. Densities of liquid and gaseous water under these condition are 1000$kg/m^3,0.60kg/m^3$ respectively. magnitude of the work done for the process is :

1. 4997 J
2. 3970 J
3. 9994 J
4. None of these

Q.

An ideal gas is taken around the cycle ABCA as shown in P-V diagram.

The net work done by the gas during the cycle is equal to:

1. $6P_1{V}_1$
2. $12P_1{V}_1$
3. $5P_1{V}_1$
4. $P_1{V}_1$

Q. If $w_1$, $w_2$, $w_3$ and $w_4$ are work done in isothermal, diabatic, isobaric and isochoric reversible processes, respectively then the correct sequence (for expansion) would be:

1. $w_1<w_2<w_3<w_4$
2. $w_3=w_2=w_1=w_4$
3. $w_3<w_2<w_4<w_1$
4. $w_3>w_1>w_2>w_4$

Q. One mole of an ideal gas $(C_v=20J{K}^{-1}mo{l}^{-1})$ initially at STP is heated at constant volume to twice the initial temperature. For the process, work done ($w$) and $q$ will be :

1. $w=0;q=5.46kJ$
2. $w=0;q=0$
3. $w=-5.46kJ;q=5.46kJ$
4. $w=5.46kJ;q=5.46kJ$

Q. One mole each of $Ca{C}_2,A{l}_4{C}_{3}andM{g}_2{C}_3$ react with $H_{2}O$ in separate open flasks at ${25}^{o}C.$ Numerical value of the work done by the system is in the order:
Given reactions:
$Ca{C}_2\left(s\right)+2H_{2}O\left(l\right)\to Ca\left(OH{)}_2\right(s)+C_2{H}_2(g)$
$A{l}_4{C}_3\left(s\right)+12H_{2}O\left(l\right)\to 4Al\left(OH{)}_3\right(s)+3C{H}_4(g)$
$M{g}_2{C}_3\left(s\right)+4H_{2}O\left(l\right)\to 2Mg\left(OH{)}_2\right(s)+C{H}_3-C\equiv CH(g)$

1. $Ca{C}_2<A{l}_4{C}_3<M{g}_2{C}_3$
2. $Ca{C}_2=M{g}_2{C}_3<A{l}_4{C}_3$
3. $Ca{C}_2<M{g}_2{C}_3<A{l}_4{C}_3$
4. $Ca{C}_2>A{l}_4{C}_3>M{g}_2{C}_3$

Q. Closed systems can exchange which of the following with the surroundings?

1. Heat
2. Matter
3. Heat and Matter
4. Neither heat nor matter