Use of the British thermal unit (Btu) is common in some types of engineering work. A Btu is the amount of heat required to raise the temperature of 1 lb of water by 1°F. Calculate the number of joules in a Btu.

Video transcript

Welcome back everyone in this example, we're told that the amount of heat needed to increase £1 of water's temperature by one F is measured in british thermal units. A quad is equal to 10 to the 15th power british thermal units. But how many jewels are in a quad is what we need to figure out. So we're going to ultimately utilize dimensional analysis. And because we're dealing with water as our substance, we want to recall that water has a specific heat value where we understand that One calorie is the amount of energy needed to heat one g of water by 1°C. So times One°C and we're going to multiply this by water specific heat capacity which we were college represented by 4.184 jewels. And this is per calorie. So far we can cancel out our units of calories and now we're left with jules para grams times degrees Celsius. So next let's focus on canceling out those units of grams by recalling that we have 453.6 g equal to £1. This allows us to now cancel our units of grams and now we're left with jules divided by degrees Celsius times pounds. But we want to recall that according to the prompt, we're going to be raising the temperature of water to one F. And right now we are at degrees Celsius. Inter dimensional analysis. So we want to recall that to convert from Celsius to Fahrenheit. We multiply our temperature in Celsius by 5/9 and so we're going to multiply by that as a conversion factor. So we can say we go from five degrees Celsius to nine F and because we have Celsius in the numerator and then in the denominator here we can cancel that out. Now. Now we can focus on getting rid of this Fahrenheit term by utilizing the info from the prompt where it tells us that one F is measured in british thermal units and so we can understand that £1 of water heated up to one F is equivalent to one british thermal unit and this comes directly from our prompt. So this allows us to not only cancel our degrees of Fahrenheit but also our pound term here since we have it in the numerator and the denominator and now we want to focus on getting quads into our units. So we're going to continue our conversion below here where we're going to recall that given in the prompt, we have 10 to the 15th power british thermal units equivalent to one quad. And now that we have british thermal units in the numerator and then in the denominator here that cancels out leaving us with jewels per quad as our final unit, which is what we want according to the prompt. And so in our calculators when we type in the product of all of our quotients, we should yield a value of one point sorry one point oh five times 10 to the 18th power jewels per quad. Now looking at our prompt, we see that our smallest number of Sig figs is too sick fix. And so we're going to say that this is equal to about 1.1 times 10 to the 18th power jewels per quad. And so this is going to be our final answer as the amount of heat needed, Or sorry, as the amount of jewels in a quad according to our prompt. So I hope that everything I explained was clear. If you have any questions, leave them down below and I'll see everyone in the next practice video.