# Heat capacity (video)

## Video transcript

– [ Instructor ] The heat capacity of an object is the come of heat necessity to raise the temperature of the object by one degree Celsius or one Kelvin. The specific heat capacity, which is often just called specific estrus is the heat capacity of one gram of a substance while the molar heating system capacitance is the heat capacity for one mole of a message. We symbolize specific inflame with a capital C and a subscript s for specific, and molar heating system capacity is symbolized by capital C with a subscript m. First lashkar-e-taiba ‘s look at specific heat. The particular heat of body of water is equal to 4.18 joules per gram degrees Celsius. And what this means is if we have one gram of liquid body of water, and let ‘s say the initial temperature is 14.5 degrees Celsius, it takes positive 4.18 joules of energy to increase the temperature of that one gram of water by one degree Celsius. Therefore the final examination temperature of the water would be 15.5 degrees Celsius after we add 4.18 joules. future let ‘s calculate the molar heat capability of water from the specific heat. If we multiply the specific inflame of urine by the molar multitude of water which is 18.0 grams per mole, the grams will cancel out and that gives us 75.2 joules per counterspy degree Celsius. And so this is the molar inflame capacity of water. Let ‘s say we had 18.0 grams of urine. If we divide by the molar mass of water which is 18.0 grams per mole, the grams cancel and that gives us one counterspy of liquid water. So one counterspy of H2O. Using the molar heating system capacity of water, it would take plus 75.2 joules of department of energy to increase the temperature of that 18.0 grams of urine by one degree Celsius. Next let ‘s calculate how much inflame is necessary to warm 250 grams of water from an initial temperature of 22 degrees Celsius to a concluding temperature of 98 degrees Celsius. Using the units for specific hotness, which are joules per gram degree Celsius. We can rewrite the specific inflame is equal to joules is the quantity of heat that ‘s transferred. So we could precisely write q for that. Grams is the batch of the substance and degree Celsius is talking about the change in temperature delta T. so if we multiply both sides by molarity delta T, we arrive at the following equality which is q is equal to mC delta T. And we can use this equality to calculate the heat transferred for different substances with unlike specific heats. however, right now we ‘re only interested in our liquid body of water and how much heat it takes to increase the temperature of our water from 22 degrees Celsius to a final examination temperature of 98 degrees Celsius. To find the change in temperature, that ‘s equal to the final temperature minus the initial temperature which would be 98 degrees Celsius minus 22 which is equal to 76 degrees Celsius. Next, we can plug everything into our equation. Q is what we ‘re trying to find. M is the mass of the substance, which is 250 grams. C is the specific heat of water which is 4.18 joules per gram degrees Celsius, and delta T we ‘ve good found is 76 degrees Celsius. So let ‘s plug everything into our equality. Q would be equal to, the mass is 250 grams. The specific heat of water is 4.18 joules per gram degree Celsius. And the change of temperature is 76 degrees Celsius. so looking at that, we can see that grams will cancel out and degrees Celsius will cancel out and give us, q is equal to 79,420 joules or to two significant figures, q is equal to 7.9 times 10 to the fourth joules. so 7.9 times 10 to the one-fourth joules of energy has to be transferred to the water to increase the temperature of the body of water from 22 degrees Celsius to 98 degrees Celsius. The specific estrus can vary slightly with temperature. So the temperature is much specified when you ‘re looking at a postpone for specific heats. For exemplar, in the left column we have different substances, on the properly column we have their specific heats at 298 Kelvin. So we could use for our units for specific estrus joules per gram degrees Celsius, or we could use joules per gram Kelvin. For liquid urine, the specific heat is 4.18 at 298 Kelvin. For aluminum, solid aluminum, the particular hotness is 0.90. And for solid iron the specific heat is 0.45 joules per gram Kelvin. Let ‘s compare the two metals on our mesa here. Let ‘s compare a solid aluminum and solid iron. So we ‘re gon na add 1.0 times 10 to the second joules of energy to both metals and see what happens in terms of change in temperature. First, let ‘s do the calculation for aluminum. We ‘re doing Q is equal to mC delta T and we ‘re adding 1.0 times 10 to the second joules. And let ‘s say we had 10 grams of both of our metals. So this would be 10.0 grams of aluminum. And then we multiply that by this specific hotness of aluminum, which is 0.90. then 0.90 joules per gram Kelvin times delta T. When we do the mathematics for this, the joules will cancel out, the grams will cancel out and we would find that delta T would be equal to 11 Kelvin or 11 degrees Celsius. It does n’t actually matter which units you ‘re using here for the specific heat. following let ‘s do the same calculation for iron. So we ‘re adding the same sum of heat. then 1.0 times 10 to the second joules of energy. So we can plug that in, 1.0 times 10 to the second joules. We ‘re dealing with the same mass so we have 10.0 grams of iron but this time we ‘re using these specific heating system of iron which is 0.45 joules per gram Kelvin times delta T. So once again, joules cancels out, grams cancels out and we get that delta T is equal to 22 Kelvin, or 22 degrees Celsius. What we can learn from doing these two calculations is we had the same sum of heat added to our two substances with the bulk of the two substances was the same, the difference was their specific heats. So iron has a lower specific heat than aluminum. And since iron has a lower specific heat, it ‘s easier to change the temperature of the cast-iron. So the lower the respect for the specific inflame, the higher the transfer in the temperature, or you could besides say the higher the value for the specific hotness, the smaller the change in the temperature, and going back to our chart, urine, liquid water has a relatively high particular heat which means the temperature of water is relatively resistant to change.