1. ⇒ (MHT CET 2023 12th May Evening Shift )

A gas absorbs $150 J$ heat and expands by $300 {cm}^{3}$ against a constant external pressure $2 \times 10^{5} N m^{- 2}$ , What is $Δ U$ of the system?

A. 210 J

B. 90 J

C. 450 J

D. $-$ 300 J

Correct Option is (B)

$\begin{array}{l} 300 {cm}^{3} = 300 \times 10^{- 6} m^{3} \\ W = - P_{ext} Δ V \\ = - 2 \times 10^{5} N m^{- 2} \times (300 \times 10^{- 6} m^{3}) \\ = - 60 N m \\ = - 60 J \\ ∴ W = - 60 J \end{array}$

Now,

$\begin{aligned} ∴ Δ U & = q + P_{ex} Δ V \\ = 150 J + (- 60 J) \\ = 90 J \end{aligned}$

2. ⇒ (MHT CET 2023 12th May Morning Shift )

For reaction, ${CO}_{(g)} + \frac{1}{2} O_{2 (g)} ⟶ {CO}_{2 (g)}$

Which of the following equations is CORRECT at constant $T$ and $P$ ?

A. $Δ H < Δ U$

B. $Δ H > Δ U$

C. $Δ H = Δ U$

D. $Δ H = 0$

Correct Option is (A)

$\begin{aligned} Δ H = Δ U + Δ n_{g} R T \\ Δ n_{g} = 1 - (1 + 0.5) = - 0.5 \\ Δ H = Δ U - 0.5 \\ \Rightarrow Δ H < Δ U \end{aligned}$

$Δ n_{g} = - ve \Rightarrow Δ H < Δ U$

Therefore, option (A) is correct.

3. ⇒ (MHT CET 2023 11th May Morning Shift )

What is the value of increase in internal energy when system does $8 J$ of work on surrounding by supplying $40 J$ of heat to it?

A. 23 J

B. 32 J

C. 40 J

D. 48 J

Correct Option is (B)

Heat $(Q) = + 40 J$

Work $(W) = - 8 J$

According to first law of thermodynamics,

$\begin{aligned} Δ U = Q + W \\ Δ U = (+ 40 - 8) J ∴ Δ U = + 32 J \end{aligned}$

4. ⇒ (MHT CET 2023 11th May Morning Shift )

Which among the following is TRUE for isobaric process?

A. $Δ U = 0$

B. $- Δ U = - W$

C. $Δ U = Q$

D. $Q_{P} = Δ U + P_{ext} Δ V$

Correct Option is (D)

When chemical reactions are carried out in the open containers under constant atmospheric pressure (isobaric process), $Δ V \neq 0$ .

$W = - P_{ext} Δ V$

The mathematical expression of first law of thermodynamics is $Δ U = Q + W$ .

$\begin{array}{ll} ∴ & Δ U = Q_{P} - P_{ext} Δ V \\ ∴ & Q_{P} = Δ U + P_{ext} Δ V \end{array}$

5. ⇒ (MHT CET 2023 10th May Morning Shift )

The difference between $Δ H$ and $Δ U$ is usually significant for systems consisting of :

A. only solids

B. only gases

C. only liquids

D. both solids and liquids

Correct Option is (B)

Currently no explanation available

⇒Thermodynamics