Does cooling a pint glass down before putting beer in make any difference? As the title says, how much heat would you actually 'save' by cooling a glass down before putting a pint of beer in it?
I know it has to do with specific heat capacity, but I'm unsure of how to make the calculation.
My gut instinct tells me that a glass at room temperature, filled with cold beer will barely get much warmer than a glass that's at room temperature.
Thanks in advance.
 A: Prompted by @David_Z, I'll expand my comment into an answer. Let's assume that the beer and glass reach thermal equilibrium before much energy exchange with the environment. Then we can assume that there's a single final temperature $T_\mathrm{final}$, and we can apply conservation of energy $U$ to say that the same amount of energy lost by the glass or beer is gained by the other. Finally, we have the equation of state for each component $\Delta U=mc_P\Delta T$, where $m$ is the mass and $c_P$ is the constant-pressure specific heat capacity, which we'll assume is constant for simplicity.
From $\Delta U_\mathrm{glass}+\Delta U_\mathrm{beer}=0$, we have $$T_\mathrm{final}=\frac{m_\mathrm{glass}c_{P,\mathrm{glass}}T_\mathrm{glass,\,initial}+{m_\mathrm{beer}c_{P,\mathrm{beer}}T_\mathrm{beer,\,initial}}}{m_\mathrm{glass}c_{P,\mathrm{glass}}+m_\mathrm{beer}c_{P,\mathrm{beer}}}$$
Let's say the pint glass (specific heat 800 J/kg K) and the beer (specific heat 4200 J/kg K, temperature 5°C) each weigh 0.5 kg. If the glass starts at room temperature (20°C), then the beer and glass end up at 7.4°C. If the glass comes out of the freezer at -5°C, then they end up 3.4°C, or 4°C cooler. Whether this will substantially affect your drinking experience is a question only you can answer—I'll drink beer at any temperature.
