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We consider a thermodynamic system. If ΔU represents the increase in its internal energy and W the work done by the system, which of the following statements is true ?

ΔU = –W in an adiabatic process

ΔU = W in an isothermal process

ΔU = –W in an isothermal process

ΔU = W in an adiabatic process

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Explanation

According to the first law of thermodynamics

$Δ Q = Δ U + Δ W$

In adiabatic process $Δ Q = 0$ , hence $Δ U = - Δ W$

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The volume of a gas is reduced adiabatically to $\frac{1}{4}$ of its volume at 27°C, if the value of γ = 1.4, then the new temperature will be -

350 × 4^0.4K

300 × 4^0.4 K

150 × 4^0.4 K

None of these

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Explanation

For adiabatic change $T V^{γ - 1}$ = constant

⇒ $\frac{T_{2}}{T_{1}} = {(\frac{V_{1}}{V_{2}})}^{γ - 1}$ ⇒ $T_{2} = {(\frac{V_{1}}{V_{2}})}^{γ - 1} \times T_{1}$

⇒ $T_{2} = {(\frac{V}{V / 4})}^{1 .4 - 1} \times 300 = 300 \times {(4)}^{0 .4} K$

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For an adiabatic expansion of a perfect gas, the value of $\frac{Δ P}{P}$ is equal to

$- \sqrt{γ} \frac{Δ V}{V}$

$- \frac{Δ V}{V}$

$- γ \frac{Δ V}{V}$

$- γ^{2} \frac{Δ V}{V}$

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Explanation

$P V^{γ} =$ constant : Differentiating both sides

$P γ V^{γ - 1} d V + V^{γ} d P = 0 \Rightarrow \frac{d P}{P} = - γ \frac{d V}{V}$

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A gas expands under constant pressure P from volume V₁ toV₂. The work done by the gas is

$P (V_{2} - V_{1})$

$P (V_{1} - V_{2})$

$P (V_{1}^{γ} - V_{2}^{γ})$

$P \frac{V_{1} V_{2}}{V_{2} - V_{1}}$

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Explanation

Work done $= P Δ V = P (V_{2} - V_{1})$

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When heat in given to a gas in an isobaric process, then

The work is done by the gas

Internal energy of the gas increases

Both (1) and (2)

None from (1) and (2)

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Explanation

When heat is supplied at constant pressure, a part of it goes in the expansion of gas and remaining part is used to increase the temperature of the gas which in turn increases the internal energy.

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One mole of a perfect gas in a cylinder fitted with a piston has a pressure P, volume V and temperature 273 K. If the temperature is increased by 1 K keeping pressure constant, the increase in volume is

$\frac{2 V}{273}$

$\frac{V}{91}$

$\frac{V}{273}$

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Explanation

For isobaric process $\frac{V_{2}}{V_{1}} = \frac{T_{2}}{T_{1}} \Rightarrow V_{2} = V \times \frac{274}{273}$

Increase $= \frac{274 V}{273} - V = \frac{V}{273}$

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Unit mass of a liquid with volume V₁ is completely changed into a gas of volume V₂ at a constant external pressure P and temperature T. If the latent heat of evaporation for the given mass is L, then the increase in the internal energy of the system is -

Zero

$P (V_{2} - V_{1})$

$L - P (V_{2} - V_{1})$

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Explanation

$Δ Q = Δ U + P Δ V$

⇒ mL = ΔU + P(V₂ – V₁)

⇒ ΔU = L – P (V₂ – V₁) (âˆµ m = 1)

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A gas expands 0.25m³ at constant pressure 10³ N/m², the work done is -

2.5 ergs

250 J

250 W

250 N

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Explanation

$Δ W = P Δ V = 10^{3} \times 0 .25 = 250 J$

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If 300 ml of a gas at 27°C is cooled to 7°C at constant pressure, then its final volume will be -

540 ml

350 ml

280 ml

135 ml

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Explanation

V ∝ T at constant pressure

⇒ $\frac{V_{1}}{V_{2}} = \frac{T_{1}}{T_{2}}$

⇒ $V_{2} = \frac{V_{1} T_{2}}{T_{1}} = \frac{300 \times 280}{300} = 280 m l .$

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Which of the following is correct in terms of increasing work done for the same initial volume and final volume ?

Adiabatic < Isothermal < Isobaric

Isobaric < Adiabatic < Isothermal

Adiabatic < Isobaric < Isothermal

None of these

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Yes. You can attempt every Physics question on this page for free without logging in, and check the correct answer with a detailed explanation instantly.

No account is required to attempt questions and view answers. A free account adds bookmarks, personal notes, and progress tracking.

The bank mixes NEET previous year questions (PYQs) with practice questions, each tagged with its exam appearances where applicable.