Please help with #6, #7, #8 I need solution! Answer for #6 - c Answer for #7 - b
ID: 1780694 • Letter: P
Question
Please help with #6, #7, #8 I need solution!
Answer for #6 - c
Answer for #7 - b
Answer for #8 - a
6) An additional 2000-kg mass is placed on the cap, which causes the cylinder to finally contract to a final equilibrium height of 15 cm. Compute the new temperature of the gas contained within the shorter cylinder. Assume the cylinder is in contract with an appropriate thermal reservoir, i.e., that heat can flow in or out of the gas. Assume g = 9.8 m/s2 .
7) Which is true for the Q of the gas during this process when the cap finally comes to rest at it's new equilibrium height of 15 cm. Note that the work done on the gas is mg h .
8) If instead the container is perfectly insulated to ensure no heat flows in or out, what happens to the final temperature of the gas when the 2000-kg mass is added to the cap?
The next four problems are related. Consider 10 moles of nitrogen within a cylinder with a cross sectional area of 1 m2 Assume that the cover ("cap") of the cylinder, is a disk which can slide frictionlessly within the cylinder. Assume that the cap makes a “leak-proof" fit so that 10 moles of nitrogen always exist within the cylinder, independent of the cap height. The gas in the cylinder has pressure 120x10 Pa (hint: what does that say about the external pressure?). 5. The initial height of the cylinder is 20.8 cm; find the temperature of the gas. a. 473.3 K b. 600.6 K c. 350.3 K d. 300.2 K e. 377.6K 20.8 cm 6. An additional 2000-kg mass is placed on the cap, which causes the cylinder to finally contract to a final equilibrium height of 15 cm. Compute the new temperature of the gas contained within the shorter cylinder. Assume the cylinder is in contract with an appropriate thermal reservoir, i.e., that heat can flow in or out of the gas. Assume g = 9 .8 m/s. 15 cm a. 150.3 K b. 175.2 K c. 251.9 K d. 225.1 K e. 269.6 K 7. Which is true for the Q of the gas during this process when the cap finally comes to rest at it's new equilibrium height of 15 cm. Note that the work done on the gas is mg Ah a. Q>0 c, Q = 0 8. Ifinstead the container is perfectly insulated to ensure no heat flows in or out, what happens to the final temperature of the gas when the 2000-kg mass is added to the cap? a. The temperature increases. c. There is no change in the temperature.Explanation / Answer
6) Area = 1 m2, additional force,F =mg= 2000*9.8= 19600 N
additional pressure, P2= F/A = 19600/1 = 19600 Pa
total pressure,P = initial pressure + P2 = 120000+19600 = 139600 Pa
volume= height*area = 0.15*1 = 0.15 m3
Using ideal gas law,
PV=nRT
T=PV/nR
T=139600*0.15 / 10*8.314
T=251.9 K
7) From first law of thermodynamics,
Q=U+W
U is internal energy = cv*dT
since dT is negative(temperature decreases) hence U is negative
Work done = mg*dh; here dh is also negative as the height decreases, hence W is also negative
since U and W are both negative hence from the first law, Q should also be negative
Q<0
8) since there is no heat flow hence,
U= -W
Since W is negative hence, U should be positive
now if U is positive , hence dT should also be positive ; dT>0
dT= Tfinal - Tinitial
Tfinal - Tinitial > 0
Tfinal >Tinitial
hence temperature increases.
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