Lost Heat

When q hot + q cold ≠ 0 We have made the assumption that all heat is transferred, whether that’s objects or reactions. This is a ridiculous assumption: No container perfectly insulates.

How much? Finding out how much heat is lost is actually pretty easy: q hot + q cold + q lost = 0 Or q reaction + q water + q lost = 0

How much? Now substitute: q hot + q cold + q lost = 0 mc  T + mc  T + q lost = 0 Or q reaction + q water + q lost = 0  H*moles + mc  T + q lost = 0

How much? Now substitute: q hot + q cold + q lost = 0 mc  T + mc  T + q lost = 0 Or q reaction + q water + q lost = 0  H*moles + mc  T + q lost = 0 If you measure everything else, q lost can be found.

For Example Mix 15g of hot water (77 o C) with 22g of cold water (22 o C). If the final temperature is 36 o C, then… q hot + q cold + q lost = 0

For Example Mix 15g of hot water (77 o C) with 22g of cold water (22 o C). If the final temperature is 38 o C, then… q hot + q cold + q lost = 0 15*4.184*(-39) + 22*4.184*16 + q lost = 0

For Example Mix 15g of hot water (77 o C) with 22g of cold water (22 o C). If the final temperature is 38 o C, then… q hot + q cold + q lost = 0 15*4.184*(-39) + 22*4.184*16 + q lost = 0 q lost = 975 J The hot water produced 2448 J The cold water absorbed 1473 J

Fair Comparisons Mix 15g of hot water (77 o C) with 22g of cold water (22 o C). If the final temperature is 38 o C, then… q hot + q cold + q lost = 0 15*4.184*(-39) + 22*4.184*16 + q lost = 0 q lost = 975 J Just like with reactions, comparing q lost probably isn’t fair unless we standardize the number. In this case, we’ll do it per degree (assuming the container also started at 22 o C): 975 J / 16 o C = 61 J/ o C = C cal

What is C cal ? Just like with reactions, if q lost /  T = C cal then q lost = C cal *  T C cal is a measure of how well a container insulates–’for every degree that the contents heat up, how much heat is lost?’ (or, ‘for every degree that the contents cool down, how much extra heat the container provide?’)

Why cal? The ‘cal’ is short for ‘calorimeter’, which essentially means “a container that you do a heat transfer experiment in”. A perfect calorimeter would have C cal = 0 J/ o C Note: this value covers all the heat lost in your setup to everything—cup, air, thermometer, zombies—so long as you keep your setup reasonably the same.

Summary Heat lost is just another q Find it by measuring all the other q values q = C cal *  T There are now three choices for what to substitute in for q: object, reaction, or calorimeter.