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Q.

The pressure of a monoatomic gas increases linearly from $4 \times 10^{5} P a t o 8 \times 10^{5} P a$ when its volume increases from 0.2 $m^{3}$ to 0.5 $m^{3}$ then increase in internal energy in joule is

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a

$4.8 \times 10^{4}$

b

$2.4 \times 10^{5}$

c

$4.8 \times 10^{5}$

d

$6.8 \times 10^{4}$

answer is A.

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Detailed Solution

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Change in internal energy of a gas is given by $∆ U = n C_{v} d T = \frac{n R}{γ - 1} (T_{2} - T_{1}) = \frac{P_{2} V_{2} - P_{1} V_{1}}{γ - 1}$

As the gas is monoatomic, g = 5/3

So $∆ U = 10^{5} (\frac{8 \times 0.5 - 4 \times 0.2}{\frac{5}{3} - 1}) = \frac{3}{2} \times 3.2 \times 10^{5} = 4.8 \times 10^{5}$

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