Problem 17.53 Part A A cube 23 cm on each side contains 2.5 g of helium at 20 °C
ID: 1518758 • Letter: P
Question
Problem 17.53 Part A A cube 23 cm on each side contains 2.5 g of helium at 20 °C. 1000 J of heat energy are transferred to this gas. What is the final pressure if the process is at constant volume? Express your answer to two significant figures and include the appropriate units p= 1.6-10, Pa Submit My Answers Give Up Incorrect; Try Again; 18 attempts remaining Part B What is the final volume if the process is at constant pressure? Express your answer to two significant figures and include the appropriate units v= Value Units Submit My Answers Give Up Provide Feedback ContinueExplanation / Answer
At a constant volume, the extra heat raises the temperature of the He. Its higher temperature, in turn, would correspond to a higher pressure.
Cv = (3/2)R for a monatomic gas
Cv = (3/2)(8.314 J/mol-K)
Cv = 12.47 J/mol-K
1000 J = (2.5 g)(mol He / 4 g)(12.47 J/mol-K)(T)
T = 128.3 K
new T = 273 + 20 + 128.3 K
new T = 421.3 K
old p = nR(old T)/V
old p = (2.5 g)(mol / 4.0 g)(8.314 J/mol-K)(20 + 273 K) / (0.23^3 m^3)
old p = 1.251 e5 Pa
(old p)/(old T) = (new p)/(new T)
(1.251e5 Pa)/(293 K) = (new p)/(421.3 K)
new p = 1.79 e5 Pa
(b)
(old V)/(old T) = (new V)/(new T)
(0.23^3 m^3)/(293 K) = (new V)/(421.3 K)
new V = 0.0174 m^3