JEE Advanced · Chemistry · 6. Thermodynamics (C)

A reversible cyclic process for an ideal gas is shown below. Here, $P, V, a n d T$ are pressure, volume and temperature, respectively. The thermodynamic parameters $q, w, H a n d U$ are heat, work, enthalpy and internal energy, respectively.

The correct option(s) is (are)

A $q_{A C} = ∆ U_{B C} a n d w_{A B} = P_{2} (V_{2} - V_{1})$
B $w_{B C} = P_{2} (V_{2} - V_{1}) a n d q_{B C} = ∆ H_{A C}$
C $∆ H_{C A} < ∆ U_{C A} a n d q_{A C} = ∆ U_{B C}$
D $q_{B C} = ∆ H_{A C} a n d ∆ H_{C A} > ∆ U_{C A}$

Verified Solution

Answer & Solution

Correct Answer

(D) $q_{B C} = ∆ H_{A C} a n d ∆ H_{C A} > ∆ U_{C A}$

Step-by-step Solution

Detailed explanation

AC → Isochoric
AB → Isothermal
BC → Isobaric

# q_{A C} = ∆ U_{B C} = n C_{V} (T_{2} - T_{1})

W_{A B} = n R T_{1} \ln (\frac{V_{2}}{V_{1}})

A (wrong)

# q_{B C} = ∆ H_{A C} = n C_{P} (T_{2} - T_{1})

W_{B C} = - P_{2} (V_{1} - V_{2})

B (correct)

# n C_{P} (T_{1} - T_{2}) < n C_{V} (T_{1} - T_{2})

C (correct)

∆ H_{C A} < ∆ U_{C A}

# D

(wrong)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From JEE Advanced

The dilution processes of different aqueous solutions with water are given in LIST-I. The effects of dilution of the solutions on

[H^{+}]

are given in LIST-II.
(Note: The degree of dissociation

(α)

of a weak acid and a weak base is

< < 1;

the degree of hydrolysis of salt is

< < 1; [H^{+}]

represents the concentration of

H^{+}

ions)

List - I	List - II
A) 10 mL of $0.1\text{ M NaOH} +20\text{ mL}$ of 0.1 M acetic acid diluted to 60 mL .	P) The value of $\left[\text H ^{+}\right]$does not change on dilution.
B) 20 mL of $0.1\text{ M NaOH} +20\text{ mL}$ of 0.1 M acetic acid diluted to 80 mL .	Q) The value of $\left[\text H ^{+}\right]$changes to half of its initial value on dilution.
C) 20 mL of $0.1\text{ M HCl} +20\text{ mL}$ of 0.1 M ammonia solution diluted to 80 mL .	R) The value of $\left[\text H ^{+}\right]$changes to two times its initial value on dilution.
D) 10 mL saturated solution of $\text{Ni} (\text{OH})_2$ in equilibrium with excess of solid $\text{Ni} (\text{OH})_2$ is diluted to 20 mL (solid $\text{Ni} (\text{OH})_2$ is still present after dilution).	S) The value of $\left[\text H ^{+}\right]$changes to $\sqrt{ }$ times its initial value on dilution.
	T) The value of $\left[\text H ^{+}\right]$changes to $\sqrt{2}$ times its initial value on dilution.

Match each process given in LIST-I with one or more effect(s) in LIST-II. The correct option is

JEE Advanced 2018 Hard

Explore more questions on app

List - I	List - II
A) 10 mL of \(0.1\text{ M NaOH} +20\text{ mL}\) of 0.1 M acetic acid diluted to 60 mL .	P) The value of \(\left[\text H ^{+}\right]\)does not change on dilution.
B) 20 mL of \(0.1\text{ M NaOH} +20\text{ mL}\) of 0.1 M acetic acid diluted to 80 mL .	Q) The value of \(\left[\text H ^{+}\right]\)changes to half of its initial value on dilution.
C) 20 mL of \(0.1\text{ M HCl} +20\text{ mL}\) of 0.1 M ammonia solution diluted to 80 mL .	R) The value of \(\left[\text H ^{+}\right]\)changes to two times its initial value on dilution.
D) 10 mL saturated solution of \(\text{Ni} (\text{OH})_2\) in equilibrium with excess of solid \(\text{Ni} (\text{OH})_2\) is diluted to 20 mL (solid \(\text{Ni} (\text{OH})_2\) is still present after dilution).	S) The value of \(\left[\text H ^{+}\right]\)changes to \(\sqrt{ }\) times its initial value on dilution.
	T) The value of \(\left[\text H ^{+}\right]\)changes to \(\sqrt{2}\) times its initial value on dilution.

A reversible cyclic process for an ideal gas is shown below. Here, P, V, and T are pressure, volume and temperature, respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and internal energy, respectively.The correct option(s) is (are)

Step-by-step Solution

A reversible cyclic process for an ideal gas is shown below. Here, $P, V, a n d T$ are pressure, volume and temperature, respectively. The thermodynamic parameters $q, w, H a n d U$ are heat, work, enthalpy and internal energy, respectively.

The correct option(s) is (are)