The figure shows an m = 75-kg frictionless cylindrical piston (with diameter d =

Question

The figure shows an m = 75-kg frictionless cylindrical piston (with diameter d = 14_cm) that floats on 0.72_mol of compressed gas at T_1 = 39 degree C. How far does the piston rise if the temperature is increased to T_2 = 420 degree C? Note that the piston itself is subject to 1 atm of external pressure. Use R = 8.314 _J/mol.K as the gas constant. 127.3_cm 181.3_cm 97.51_cm 84.8_cm 54.33_cm 161.2_cm A(n) 110-kg student eats a 175-Calorie doughnut. To burn-it-off, he decides to climb the steps of a tall build How high (in m) would he have to climb to expend an equivalent amount of work? 509.9 m 812.9 m 679.5 m 649.6 m 802.8 m 519.8 m

Explanation / Answer

4) pressure = 75* 9.8 / pi *0.07^2 = 47746.5 Pa
Important to realize that this is GAGE pressure, not absolute, (there is one atm pressure also pushing on the piston) so add 101300 Pa

P = 149046.5 Pa (absolute)
n = 0.72
R = 8.314 m^3 Pa /K mole
T = 273 + 39 = 312 K (absolute)
solving for V:
V = 0.0125 m^3

volume of cylinder = pi * r^2 * h ==========> h = 0.814 m

increasing the temperature to 420 C =====> T goes from 312 K to 693 K, or 2.22 x
So volume also increases by 2.22 x   And h also increases by 2.22x
(P, n and area are constant)

change in h = 1.22(0.814) = 0.993 meters = 99.3 (option c)

5)  As 1 food Calorie= 10^3 Calories

so, 175 food calories = 1.75* 10^5 calories = 1.75 * 10^5 * 4.186 J = 7.34*10^5 J

The work to lift a mass m up to an altitude h is W = mgh

If the student wants to expend 7.34*10^5 J, he has to climb up to
h = W/mg = 7.34*10^5/(110*9.8) = 680.9 m (option C)

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