Question

Part A A 12 cm -diameter cylinder contains argon gas at 10 atm pressure and a temperature of 50°C. A piston can slide in and out of the cylinder. The cylinder's initial length is 21 cm. 2700 J of heat are transferred to the gas, causing the gas to expand at constant pressure. What is the final temperature of the cylinder? Express your answer to two significant figures and include the appropriate units. R ? O Å Value O a degC Tribal = Submit Request Answer Part B What is the final length of the cylinder? Express your answer to two significant figures and include the appropriate units. CHÁ A O O ? lfinal = Value cm Submit Request Answer

Answer 1

Given

Argon gas in a cylinder with diameter 12 cm , radius r = 6 cm = 0.06 m

Pressure P = 10 atm = 10*1.01*10^5 Pa

initial temperature Ti = 50 0C = 50*273.15 = 323.15 k

cylinder initial length Li = 0.21 m
heat transfered is dQ = 2100 J

molar specific heat of organ at constant pressure is Cp = 20.80 J/mol.k

volume of the cylinder is V = pi*r^2*L

initial volume is Vi = pi*0.06^2*0.21 m^3

       Vi = 0.00238 m^3

dQ = n*C*dT , for number of moles , from ideal gas equation

   PV = n*RT

   n = PV/RT

   n = (10*1.01*10^5*0.00238)/(8.314*323.15)

   n = 0.89471

Part A

for final temperature , Tf = ?

   dT = dQ/(n*C)

   dT = 2100/(0.89471*20.80) k

   dT =112.843 k

   Tf -Ti = 112.843 k
   Tf = 112.84275 +323.15 k

   Tf = 436 k

Part B
for final length of the cylinder Lf , from ideal gas equation

   P*Vf = n*R*Tf

   P*pi*r^2*Lf = n*R*Tf

   Lf = n*R*Tf/(P*pi*r^2)

   Lf = (0.89471*8.314*436)/(10*1.01*10^5*pi*0.06^2) m

   Lf = 0.28393 m

   Lf = 28.4 cm