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Heat and Thermodynamics

Section: Physics

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Question : 23 of 78

Marks: +1, -0

If a gas of volume 400 cc at an initial pressure

P

is suddenly compressed to 100 cc , then its final pressure is (The ratio of the specific heat capacities of the gas at constant pressure and constant volume is 1.5 )

[AP EAPCET 21 May 2025 S2]

$\; \frac{P}{32}$
8 P
32P
16P

Solution:

Given:

Initial volume

V_1=400\ \text{cc}

Final volume

V_2=100\ \text{cc}

Initial pressure

P_1=p

The process is sudden (adiabatic)

Thus, for an adiabatic process:

P_1 V_1^\gamma = P_2 V_2^\gamma

Given:

\gamma = 1.5

Step 1: Write the equation for

P_2

P_2 = P_1 \left( \frac{V_1}{V_2} \right)^\gamma

Step 2: Substitute the values

P_2 = p \left( \frac{400}{100} \right)^{1.5} = p(4)^{1.5}

Step 3: Simplify

(4)^{1.5} = 4^1 \times 4^{0.5} = 4 \times 2 = 8

P_2 = 8p

Final Answer:

P_2 = 8p

Correct Option: (B)

8p

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