# Homework Help: Thermal Expansion of ethanol

1. May 21, 2010

### pat666

1. The problem statement, all variables and given/known data
1. You pour 108 cm^3 of ethanol, at a temperature of - 10.0 C, into a graduated cylinder initially at 20.0 C, filling it to the very top. The cylinder is made of glass with a specific heat of 840 J/kgK and a coefficient of volume expansion of 1.2 × 10^-5 K^-1; its mass is 0.110 kg. The mass of the ethanol is 0.0873 kg. The specific heat capacity of ethanol is 2428 J/kgK and the coefficient of volume expansion of ethanol is 7.5 × 10-^5 K^-1.
(a) What will be the final temperature of the ethanol, once thermal equilibrium is reached?
(b) How much ethanol will overflow the cylinder before thermal equilibrium is reached?

2. Relevant equations

Q_e+Q_g=0
m_g c_g (T_f-T_gi )+m_e c_e (T_f-T_ei )=0
ΔV/V=βΔT
3. The attempt at a solution

Ive solved them - i really need someone to check them for me, i got - 0.892C for a which i think is right and 0.1cm^3 for b. I am really unsure of b. To solve b i found the expansion of the glass to be -2.71*〖10〗^(-8) m^3 and therefore the final volume to be 1.0797*〖10〗^(-4)m3 then i did the same for the ethanol which i got 7.38*〖10〗^(-8)m3 and 1.0807*〖10〗^(-4)m3 respectively..... from that i found V_loss=V_fe-V_fg and then i got the answer of 0.1 cm3........... any help is appreciated

2. May 21, 2010

### RTW69

The ethanol is heating up from 10 C and the glass is cooling down from 20 C so you should get a final temperature some where in between so I don't see your final temperature of .89 C. The over flow equals the volume expansion of the ethanol plus the volume contraction of the glass.

3. May 21, 2010

### pat666

sorry thats my bad typing. its heating up from minus 10 degrees and cooling down from 20 degrees and my answer is minus 0.892 degrees. all Celsius for part a.