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Q.

A gas at a pressure of 5.0 atm is heated from $0^{0} to 546^{0} C$ and simultaneously compressed to one-third of its original volume. Hence final pressure is

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a

30.0 atm

b

10.0 atm

c

5.0 atm

d

45.0 atm

answer is C.

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Detailed Solution

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$P_{1} = 5.0 atm, T_{1} = 0^{0} C = 273 K, T_{2} = 546^{o} C = 819 K, V_{2} = \frac{1}{3} V ∴ From \frac{P_{1} V_{1}}{P_{2} V_{2}} = \frac{T_{1}}{T_{2}} \frac{5 \times V}{P_{2} \times \frac{1}{3} V} = \frac{273}{819} \frac{5 \times 3}{P_{2}} = \frac{1}{3} P_{2} = 45 atm$

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