6. (10 points) An aluminum canister has a volume of exactly two liters at 20°C.

Question

6. (10 points) An aluminum canister has a volume of exactly two liters at 20°C. It is filled with helium gas and has an absolute pressure of 160,000 Pa and a temperature of 20°C. (a) Now the canister is heated to a temperature of 200°C. Neglecting the expansion of the gas canister (assume V = two liters), find the new absolute pressure within the gas (b)* Now take the expansion of the canister into account. What is the actual volume of the canister when it is heated to 200°C? (Aluminum has a coefficient of linear expansion of 25x10 °C and a coefficient of volume expansion of 75x10 PC.) Using this volume, what is the actual absolute pressure inside of the canister when heated to 200°C?

Explanation / Answer

V = 2 x 10^-3 L

T = 273 + 20 = 293 K  

P = 160000 Pa

(A) Tf = 273 + 200 = 473 K  

Pi / Ti = Pf / Tf

Pf = (160,000) (473/293)

Pf = 258294 Pa

(b) Vf = V0 (1 + (75 x 10^-6 x 180))

Vf = 1.0135 V0

P V / T = Pf Vf / Tf

(160,000) ( V0) / (293) = Pf (1.0135 V0) / 473

Pf = 254853 Pa

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