Thermodynamics

JEE Main level, numerical answer, medium

67 of 190

Question 67 of 190

An insulated cylinder of volume 60 cm360 \mathrm{~cm}^{3} is filled with a gas at 27∘C27^{\circ} \mathrm{C} and 2 atmospheric pressure. Then the gas is compressed making the final volume as 20 cm320 \mathrm{~cm}^{3} while allowing the temperature to rise to 77∘C77^{\circ} \mathrm{C}. The final pressure is ____\_\_\_\_ atmospheric pressure.

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Answer: 7

PV=nRTPV = nRT
P1V1RT1=P2V2RT2\dfrac{P_1 V_1}{RT_1} = \dfrac{P_2 V_2}{RT_2}
2×105×60300=P2×20350\dfrac{2 \times 10^5 \times 60}{300} = \dfrac{P_2 \times 20}{350}
P2=2×105×7×36P_2 = \dfrac{2 \times 10^5 \times 7 \times 3}{6}
P2=7×105=7 atmP_2 = 7 \times 10^5 = 7 \text{ atm}

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