Thermodynamics NEET PYQ with Solutions

Q 1 :
Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radius $r_{A}$ and $r_{B}$ , respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas A and B are displaced by 16 cm and 9 cm, respectively. If the change in their internal energy is the same, then the ratio $\frac{r_{A}}{r_{B}}$ is equal to [2025]

$\frac{2}{\sqrt{3}}$
$\frac{\sqrt{3}}{2}$
$\frac{4}{3}$
$\frac{3}{4}$

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4

(4)

Given, pressure, $P = constant \Rightarrow P_{A} = P_{B}$

Also, $Δ U_{A} = Δ U_{B}$

From first law of thermodynamics

$Δ Q_{A} = Δ U_{A} + Δ W_{A}$

$\Rightarrow Δ Q_{A} = Δ U_{A} + P_{A} (16) \times A_{A}$ ...(i)

$Δ Q_{B} = Δ U_{B} + Δ W_{B}$

$\Rightarrow Δ Q_{B} = Δ U_{B} + P_{B} (9) \times A_{B}$ ...(ii)

Given $Δ Q_{A} = Δ Q_{B}$

$\Rightarrow Δ U_{A} + P_{A} (16) A_{A} = Δ U_{B} + P_{B} (9) \times A_{B}$

$\Rightarrow 16 \times π \times r_{A}^{2} = 9 \times π \times r_{B}^{2}$

$\Rightarrow {(\frac{r_{A}}{r_{B}})}^{2} = \frac{9}{16} \Rightarrow \frac{r_{A}}{r_{B}} = \frac{3}{4}$

Q 2 :
A thermodynamic system is taken through the cycle $a b c d a$ . The work done by the gas along the path $b c$ is [2024]

[IMAGE 102]

zero
30 J
- 90 J
- 60 J

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(1)

As volume is constant along the path $b c$ , it is an isochoric process.

[IMAGE 103]

From 1st law of thermodynamics, work done for isochoric process is, $W = P Δ V$

As, $Δ V =$ constant, so $W = 0$ $J$

Q 3 :
A sample of 0.1 g of water at $100 ° C$ and normal pressure $(1.013 \times 10^{5} {N m}^{- 2})$ requires 54 cal of heat energy to convert to steam at $100 ° C$ . If the volume of the steam produced is $167.1$ $cc$ , the change in internal energy of the sample is [2018]

104.3 J
208.7 J
42.2 J
84.5 J

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(2)

Using first law of thermodynamics, $Δ Q = Δ U + Δ W$

$\Rightarrow 54 \times 4.18 = Δ U + 1.013 \times 10^{5} (167.1 \times 10^{- 6} - 0)$

$\Rightarrow Δ U = 208.7$ $J$

Topic Question Set

Q 2 :
A thermodynamic system is taken through the cycle $a b c d a$ . The work done by the gas along the path $b c$ is [2024]

[IMAGE 102]

Q 3 :
A sample of 0.1 g of water at $100 ° C$ and normal pressure $(1.013 \times 10^{5} {N m}^{- 2})$ requires 54 cal of heat energy to convert to steam at $100 ° C$ . If the volume of the steam produced is $167.1$ $cc$ , the change in internal energy of the sample is [2018]

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Topic Question Set

Q 2 : A thermodynamic system is taken through the cycle abcda. The work done by the gas along the path bc is [2024] [IMAGE 102]

Q 3 : A sample of 0.1 g of water at 100°C and normal pressure (1.013×105 N m-2) requires 54 cal of heat energy to convert to steam at 100°C. If the volume of the steam produced is 167.1 cc, the change in internal energy of the sample is [2018]

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Q 2 :
A thermodynamic system is taken through the cycle $a b c d a$ . The work done by the gas along the path $b c$ is [2024]

[IMAGE 102]

Q 3 :
A sample of 0.1 g of water at $100 ° C$ and normal pressure $(1.013 \times 10^{5} {N m}^{- 2})$ requires 54 cal of heat energy to convert to steam at $100 ° C$ . If the volume of the steam produced is $167.1$ $cc$ , the change in internal energy of the sample is [2018]