2.- A 355 ml glass of water on a hot day in Mexico City (30 degrees celcius), yo

Question

2.- A 355 ml glass of water on a hot day in Mexico City (30 degrees celcius), you add three ice cubes of 2 cm3 apiece at 0 degrees celcius. What will be the final temperature of your drink? Consider the density of water and the same ice (1g/cm3).

3.- tells us about zero law, first law and second law of thermodynamics?

4.- calculate the work done by one mole of gas during a quasistatic isothermal expansion from an initial volume Vi to final volume Vf. When the equation of state is:

P(v-b)= RT (R,b= constan)

Explanation / Answer

n = 2 moles
T1 = 200 K
T2 = 250 K
Cv = 275 J/mol*K

Adiabatic reversible means Q = 0 and pv^k= C, k = Cp/Cv

Calculate Q
Q = 0

Calculate Work, W. Use energy balance,
?U = Q - W, Q = 0
n*Cv*?T = -W
W = -(2*275*[250-200])
W = - 27500 J = - 27.5 kJ (negative indicates process of compression)

Calculate ?U,
?U = -W = 27.5 kJ

Calculate ?H
?H = Cp?T
For diatomic gas Cv = 5/2 R so Cp = 7/2 R
So, R = 2/5*Cv = 0.4*275 J/mol.K = 110 J/mol.K
Cp = 7/2R = 385 J/mol.K
Hence, ?H = nCp?T = 2*385*50 = 38500 J = 38.5 kJ

Calculate ?S
?S = n*[Cv ln (T2/T1) - R ln(V2/V1)]
Calculate V2/V1 first.
V2/V1 = (T2/T1)^1/(k-1), k=cp/cv = 1.4
V2/V1 = (250/200)^(1/0.4)
V2/V1 = 1.747
So,
?S = 2*[275 ln (250/200) - 110*ln(1.747)]
?S = 9.0536*10^-3 J/K

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