Work Done in Isothermal Reversible Process

Q. One mole of an ideal gas at 300 K is expanded isothermally from an initial volume of 1 litre to 10 litres. The value of $△U$ for this process is:
$(R=2calmo{l}^{-1}{K}^{-l})$

1. 163.7 cal
2. zero
3. 138.1 cal
4. 9 atm L

Q. The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?

1. $T_1=T_2$
2. $T_3>T_1$
3. $W_{\text{isothermal}}>W_{\text{adiabatic}}$
4. $\Delta U_{\text{isothemal}}>\Delta U_{\text{adibatic}}$

Q. How much work in $kJmo{l}^{-1}$ unit is done by reversible and isothermal expansion of $1.2$ mole of an ideal gas to $10$ times of its original volume at ${27}^{o}C$ ?

1. $4.191$
2. $6.892$
3. $-6.892$
4. $-4.191$

Q. The molar heat capacity of water at constant pressure, $C_{p,m}$ is $75J{K}^{-1}mo{l}^{-1}$. when $1.0kJ$ of heat is supplied to $100g$ of water which is free to expand, increase in the temperature of water is:

1. $4.8K$
2. $6.6K$
3. $1.2K$
4. $2.4K$

Q. Calculate $q,w,\Delta U$ for the isothermal reversible expansion of 1 mole of an ideal gas from an initial pressure of $1.0bar$ to a final pressure of $0.1bar$ at a constant temperature of $273K$.

1. $q=-w=5.22\text{kJ}\text{and}\Delta U=0$
2. $q=-w=6.22\text{kJ}\text{and}\Delta U=0$
3. $w=q=5.22\text{kJ}\text{and}\Delta U=0$
4. $w=q=\Delta U=0$

Q. The work done in erg for the reversible expansion of $1mole$ of an ideal gas from a volume of $10litres$ to $20litres$ at ${25}^{o}C$ is

1. $2.303\times 298\times 0.082log2$
2. $-298\times {10}^7\times 8.314\times 2.303log2$
3. $-2.303\times 298\times 0.082log0.5$
4. $2.303\times 298\times 2log2$

Q. The work done by $100calorie$ of heat in isothermal expansion of ideal gas is:

1. $-418.4J$
2. $41.84J$
3. $-4.184J$
4. None of these

Q. Find the work done when $2$ moles of hydrogen expands isothermally from $15$ L to $50$ L against a constant pressure of 1 atm at ${25}^{0}C$.

1. $820.8cal$
2. $-848.2cal$
3. $84.7cal$
4. $-848.2kcal$

Q. Calculate the work done when $2moles$ of hydrogen expand isothermally and reversibly at $25{}^{\circ }C$ from $15to45litres$.

1. $-1309calories$
2. $-14.36calories$
3. $-2872calories$
4. $-28.72calories$

Q. Find the work done (in $kJ$) when one mole of the gas is expanded reversibly and isothermally from $5atm$ to $1atm$ at ${25}^{o}C$

1. $-10$ kJ
2. $-2$ kJ
3. $-8$ kJ
4. $-4$ kJ

Q.

A balloon filled with helium ($32°\mathrm{C}$ and $1.7\mathrm{atm}$) bursts. Immediately afterwards the expansion of helium can be considered as:

1. reversible isothermal

2. Irreversible isothermal

3. reversible adiabatic

4. irreversible adiabatic

Q. If a certain mass of gas is made to undergo separately adiabatic and isothermal expansion to the same pressure, starting from the same initial condition of temperature and pressure, then, as compared to that of isothermal expansion, in the case of adiabatic expansion, the final

1. volume and temperature will be higher
2. volume will be lower but the final volume will be higher
3. volume and temperature will be lower
4. temperature will be lower but the final volume will be higher

Q.

$1$ mol of an ideal gas expands reversibly and isothermally from $1\mathrm{l}$ to $100\mathrm{l}$ at $300\mathrm{K}$. The heat exchange during the process is near?

Q. Which one of the following is correct for the isothermal expansion of an ideal gas?

1. U increases but H decreases
2. U and H are unchanged
3. H increases but U decreases
4. U and H increases

Q. 5 moles of an ideal gas at ${27}^{\circ }C$ expands isothermally and reversibly from a volume of 6 L to 60 L. The work done in kJ is:

1. 14.28 kJ
2. 20.32 kJ
3. -28.72 kJ
4. -32.60 kJ

Q.

5.6 litre of helium gas at STP is adiabatically compressed to $0.7$ litre. Taking the initial temperature to be $T_1$, the work done on the gas is:

1. $\frac{9}{8}R{T}_1$
2. $\frac{9}{8}R{T}_1$
3. $\frac{3}{2}R{T}_1$
4. $\frac{15}{8}R{T}_1$

Q. $1$ mole of $C{O}_2$ gas at $300\text{K}$ is expanded under reversible adiabatic condition such that its volume becomes $27$ times the initial volume. Calculate the work done by the gas.
$(\text{Given}\gamma =1.33\text{and}{C}_V=25.08{\text{Jmol}}^{-1}{\text{K}}^{-1}\text{For}C{O}_2)$

Q. The work done by $200calorie$ of heat in isothermal expansion of ideal gas is:

1. $-836.8J$
2. $-418.4J$
3. $-555.2J$
4. $664.5J$

Q. The combination of plots which does not represent isothermal expansion of an ideal gas is:

1. B and D
2. A and D
3. B and C
4. A and C

Q. A given mass of gas expands reversibly from state A to state B by three paths 1, 2 and 3 as shown in the figure. If $w_1,w_2,and{w}_3$ respectively are the work done by the gas along three paths, then:

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

Q.

For an ideal gas, the work of reversible expansion under isothermal condition can be calculated by using the expression $W=-nRTln\frac{V_f}{V_i}$. A sample containing 1.0 mol of an ideal gas is expanded isothermally and reversible to ten times of its original volume, in two separate experiments. The expansion is carried out at 300 K and at 600 K respectively. Choose the correct option.
(a) Work done at 600 K is 20 times the work done at 300 K
(b) Work done at 300 K is twice the work done at 600 K
(c) Work done at 600 K is twice the work done at 300 K
(d) $\Delta$U = 0 in both cases

Q. Carbon monoxide is allowed to expand isothermally and reversibly from $10m^{3}to20m^3$ at $300K$ and work obtained is $4.754kJ$. Calculate the number of moles of carbon monoxide

1. $27.5mol$
2. $5.5mol$
3. $2.75mol$
4. $55.0mol$

Q. The total internal energy change for a reversible isothermal cycles is

1. Always negative
2. Always 100 calories per degree
3. 0
4. Always positive

Q.

A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume of this process is ${\mathrm{TV}}^{\mathrm{x}}=$constant, then $\mathrm{x}$ is:

1. $\frac{5}{3}$

2. $\frac{2}{5}$

3. $\frac{2}{3}$

4. $\frac{3}{5}$

Q. An ideal gas is allowed to expand against a constant pressure of $2bar$ from $10Lto50L$ in one step. Calculate the magnitude of work done by the gas. If the same expansion were carried out reversibly, will the magnitude work done be higher or lower than the earlier case? (Given that, $1Lbar=100J$)

1. $-8kJ$, lower
2. $8kJ$, lower
3. $8kJ$, higher
4. $-8kJ$ , higher

Q. Consider an ideal gas that occupies 2.50 $d{m}^3$ at a pressure of 3 bar. If the gas is compressed isothermally at a constant pressure $P_{ext}$, so that the final volume becomes 0.5 $d{m}^3$. Calculate the value of $P_{ext}$ and the work done respectively.
Given: $1bar.L$ = 100 $J$

1. $20bar$and $1000J$
2. $15bar$and $3000J$
3. $30bar$and $1500J$
4. $10bar$and $3750J$

Q. The graph given below shows the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from $(P_i,V_i)$ to $(P_f,V_f)$. Compare the work done in the above case with that carried out against a constant external pressure $P_f$.

(i) Area $AB{V}_f{V}_i$ represents total work done for a reversible isothermal expansion from $(P_i,V_i)$ to $(P_f,V_f)$.
(ii) Area $CB{V}_f{V}_i$ represents work done against a constant pressure $P_f$.

1. work (i) = work (ii)
2. work (i) > work (ii)
3. work (i) < work (ii)
4. Cannot be defined

Q.

What is reversible isothermal expansion? Give an example.

Q.

5 moles of an ideal gas expand isothermally and reversibly from a pressure of 10 atm to 2 atm at 300k. What is the largest mass which can be lifted through a height of 1 meter in this expansion?

1. 2041 kg
2. 2049 kg
3. 2409 kg
4. 4129 kg

Q. Calculate the maximum work done (in $cal$) when the pressure on 10 grams of hydrogen is reduced from $20$ to $1atm$ at a constant temperature of $273K$ if the gas behaves ideally.

1. $+8180cal$
2. $-8810cal$
3. $-8180cal$
4. $+8810cal$