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JEE Main 2014 (11 Apr, Shift 1) · P-V Diagrams & Cyclic Processes

P-V Diagrams & Cyclic Processes question from JEE Main 2014 (11 Apr, Shift 1)

Q74JEE Main 2014 · 11 APR · SHIFT 1Difficult

P-V Diagrams & Cyclic Processes

An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section 8.0 ×\times 10 −-3 m2. Initially the gas is at 300K and occupies a volume of 2.4 ×\times 10−-3 m3 and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is 1.0 ×\times 105 N/m2. The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be:

(Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible)

Figure

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Answer: (b)

  1. Final pressure P2=P0+kxA=105+8000×0.18×10−3=2×105P_2 = P_0 + \frac{kx}{A} = 10^{5} + \frac{8000 \times 0.1}{8 \times 10^{-3}} = 2 \times 10^{5} Pa.
  2. Final volume V2=2.4×10−3+8×10−3×0.1=3.2×10−3V_2 = 2.4 \times 10^{-3} + 8 \times 10^{-3} \times 0.1 = 3.2 \times 10^{-3} m3^3.
  3. T2=T1P2V2P1V1=300×2×3.22.4=800T_2 = T_1\frac{P_2V_2}{P_1V_1} = 300 \times 2 \times \frac{3.2}{2.4} = 800 K
  4. So the answer is (b) 800 K.
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