Two moles of an ideal monatomic gas are confined within a cylinder by a massless and frictionless spring loaded piston of cross-sectional area 4 xx 10^(-3)m^2. The spring is, initially, in its relaxed state. Now the gas is heated by an electric heater, placed inside the cylinder, for some time. During this time, the gas expands and does 50 J of work in moving the piston through a distance 0.10 m. The temperature of the gas increases by 50 K. Calculate the spring constant and the heat supplied by the heater.

Two moles of an ideal monatomic gas are confined within a cylinder by

1.	Two moles of an ideal monatomic gas are confined within a cylinder by a massless and frictionless spring loaded piston of cross-sectional area 4 xx 10^(-3)m^2. The spring is, initially, in its relaxed state. Now the gas is heated by an electric heater, placed inside the cylinder, for some time. During this time, the gas expands and does 50 J of work in moving the piston through a distance 0.10 m. The temperature of the gas increases by 50 K. Calculate the spring constant and the heat supplied by the heater.
Answer» Solution :`W = intPdV= int(P_0+(kx)/( A )) Adx, i.e.,W= [p_0 Ax +1/2kx^2]` ` i.e.,50 =10 ^5 xx 4 xx 10^(-5)xx 0.1xx ( 0.1 )^2 ` then ` K= 2000( N//m)` `(b )dU = nC_vd T = 2 xx 3/2R xx 50= 150xx 8.3= 1245J` Butfrom1stof thermodynamics: dQ`=dU+dW= 1245+50= 1295J.`