An ideal monoatomic gas is confined by a spring loaded massless piston of cross-section $8 \times 10^{- 3} m^{2}$ . Initially the gas is at $300 K$ and occupies a volume of $2.4 \times 10^{- 3} m^{3}$ and the spring is in its relaxed state. The gas is heated by an electric heater until piston moves out without friction by $0.1 m$ . Force constant of the spring is $8000 N / m$ , atmospheric pressure $1 \times 10^{5} {N/m}^{2}$ , the cylinder and piston are thermally insulated, the piston and spring are massless and there is no friction between the piston and cylinder. Neglect the heat lost through the wire of the heater. The heat capacity of the heater is neglected.

Find the ratio of heat supplied by the heater to the work done by the gas

Question

An ideal monoatomic gas is confined by a spring loaded massless piston of cross-section $8 \times 10^{- 3} m^{2}$ . Initially the gas is at $300 K$ and occupies a volume of $2.4 \times 10^{- 3} m^{3}$ and the spring is in its relaxed state. The gas is heated by an electric heater until piston moves out without friction by $0.1 m$ . Force constant of the spring is $8000 N / m$ , atmospheric pressure $1 \times 10^{5} {N/m}^{2}$ , the cylinder and piston are thermally insulated, the piston and spring are massless and there is no friction between the piston and cylinder. Neglect the heat lost through the wire of the heater. The heat capacity of the heater is neglected.

Find the ratio of heat supplied by the heater to the work done by the gas

Accepted Answer

Wg=12kx2+P0Ax=12×8000×(0.1)2+105×8×10−3×0.1        =40+80=120 JAlso,  Pf=P0+KxA=105+8000×0.18×10−3=2×105 Pa∵     PfVfPiVi=TfTi  ⇒     Tf=2×105×3.2×10−3105×2.4×10−3×300=800 KHeat supplied by heater=nCVΔT+Wg=105×2.4×10−3R×300×3R2×(500)+120=600+120=720JRequired ratio =720120=6  Ans

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