A polytropic process P / V = constant is carried out on 20 moles of monoatomic gas enclosed in a vertical cylinder. The cylinder is enclosed by a light piston of area 20 cm 2 at the top. The piston an

Question

A polytropic process P / V = constant is carried out on 20 moles of monoatomic gas enclosed in a vertical cylinder. The cylinder is enclosed by a light piston of area 20 cm 2 at the top. The piston and walls of the cylinder are thermally insulated but the bottom is thermally conducting having k = 2 W / mK . Its thickness is 2mm and it is kept on a reservoir maintained at a constant temperature of 400 K . The initial temperature of the gas is 300 K . Atmospheric pressure = 100 kPa . ( R = 25/3 SI units )

TestHub · Accepted Answer

Rate of heat flow: t K A ( 400 − T ) ​ = d t d θ ​ C = C v ​ + 1 − n R ​ = 2 3 ​ R + 1 + 1 R ​ = 2 R d t d Q ​ = n C d t d T ​ From (i) & (ii): t K A ( 400 − T ) ​ = n C d t d T ​ K A ∫ 0 t ​ d t d T ​ = n C ∫ 300 T ​ 400 − T d T ​ ⇒ K A ln t = − n C ln ( 100 400 − T ​ )

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